## Infinite Algebra 2

Test and worksheet generator for algebra 2.

Infinite Algebra 2 covers all typical Algebra 2 material, beginning with a few major Algebra 1 concepts and going through trigonometry. There are over 125 topics in all, from multi-step equations to trigonometric identities. Suitable for any class with advanced algebra content. Designed for all levels of learners, from remedial to advanced.

## Included in version 2.70.06 released 1/5/2023:

• Fixed: Choices could appear incorrectly

## Included in version 2.70.05 released 12/21/2022:

• Fixed: Continuous Exponential Growth and Decay Word Problems - Could generate an incorrect answer

## Included in version 2.70 released 7/8/2022:

• New: Add preferences for Metric/Imperial units
• New: Add preference to “Prefer x“ as the variable letter
• New topic: Discrete Relations
• New topic: Continuous Relations
• New topic: Evaluating and Graphing Functions
• New topic: Direct and Inverse Variation
• New topic: Continuous Exponential Growth and Decay
• Improved: UI, security, and stability with updated libraries
• Fixed: Properties of Exponents – Choices could be equivalent
• Fixed: Properties of Logarithms – Choices could be equivalent
• Fixed: Solving Exponential Equations With Logarithms – Choices could be equivalent
• Fixed: Geometric Series – Choices could be equivalent

## Included in version 2.62 released 2/8/2022:

• New: Print questions from Presentation View
• New Topic: Discrete Exponential Growth and Decay Word Problems
• Improved: UI, security, and stability with updated framework and libraries
• Improved: [Mac] Dark mode
• Fixed: [Windows] - Detached topic list does not close when application is closed
• Fixed: Probability Mutually Exclusive Word Problems - mutually exclusive case given when inappropriate

## Included in version 2.61.03 released 9/10/2021:

• Improved: Minor UI improvements
• Fixed: Law of Cosines - Crash when opening topic
• Fixed: [Windows] Unable to change page layout to landscape
• Fixed: [Windows] Error 'Unable to load platform plugin'

## Included in version 2.61 released 8/27/2021:

• Fixed: Preferences page for Kuta Works
• Improved: Security and stability with updated networking libraries

## Included in version 2.60 released 8/19/2021:

• Improved: Site licenses check expiration date more frequently
• Fixed: Combinatoric Word Problems - Values could overflow
• Fixed: Properties of Exponents - Answer might not be fully simplified
• Fixed: Properties of Logs - Possible to have duplicate choices

## Included in version 2.52 released 6/14/2019:

• New: Scramble questions by directions
• New: Scramble all questions in assignment
• New: Consolidate question sets with identical options
• New: Regroup question sets by directions
• New: Kuta Works - Create a two semester course
• New: Kuta Works - Clone assignments from a previous course into a new one
• Fixed: Presentation View - Arrow keys could change zoom at start/end of assignment
• Fixed: Tight Layout - Directions could be cramped for no reason
• Fixed: Inverse Trig - Angles limited for tan( x )
• Fixed: Inverse Trig - Errors in UI logic

## Included in version 2.50 released 4/12/2019:

• New: Kuta Works - Option to hide answers and results from students until after due date
• New: Kuta Works - Option to control how long choices are hidden
• Improved: Options windows appear at a better initial size
• Improved: Window controls shown at their native size and spacing
• Improved: Network proxy configuration window
• Fixed: Presentation View - Answers could be cut off
• Fixed: Some window controls cut off on Windows 10 with display scaling
• Fixed: Spelling errors
• Fixed: Kuta Works - Course list could display more than just your active courses
• Fixed: Graphing Rational Functions - Open holes in graph could appear as filled holes

## Included in version 2.42 released 12/11/2018:

• Fixed: Certain symbols incorrect if saved on Mac and loaded on Windows or vice versa
• Fixed: General Sequences - Recursive formula sometimes wrong
• Fixed: Properties of Logarithms - Avoid questions with reducible roots

## Included in version 2.41 released 9/26/2018:

• Fixed: Archived courses in Kuta Works are now hidden
• Fixed: Generating or regenerating questions could cause a crash

## Included in version 2.40 released 8/8/2018:

• New: Integrated with Kuta Works . Now post assignments online.

## Included in version 2.25 released 4/27/2018:

• Improved: Generate questions more quickly
• Improved: Measurement arrows reach correct endpoints
• Improved: Absolute Value Equations - Better decimal numbers
• Improved: Absolute Value Inequalities - Better decimal numbers
• Improved: Compound Inequalities - Better decimal numbers
• Improved: Multi-Step Equations - Better decimal numbers and more predictable special cases
• Improved: Multi-Step Inequalities - Better decimal numbers
• Improved: Order of Operations - Better decimal numbers
• Fixed: Trig units for piecewise functions and ordered pairs
• Fixed: Graphing Rational Functions - Prevent equivalent choices
• Fixed: Law of Sines - Program could freeze
• Fixed: Transformations - Prevent equivalent choices

## Included in version 2.18 released 7/31/2017:

• Fixed: Open circles on graphs were filled in when displayed as answer in red
• Fixed: Typo in sample custom question
• Fixed: Transformations - Program could freeze
• Fixed: Systems of Quadratic Equations - Program could freeze

## Included in version 2.17 released 4/27/2017:

• Improved: [Windows] "Export to clipboard as bitmap" renders image with better quality
• Fixed: Probability with Combinations and Permutations - Could ask about impossible lottery ball

## Included in version 2.16.20 released 11/16/2016:

• Fixed: Solving Quadratic Equations by Taking Square Roots - Option to "Allow fractions" not working as expected

## Included in version 2.16 released 9/16/2016:

• Fixed: Numbers with many significant digits could round incorrectly
• Fixed: Customized question containing an error could not be modified
• Fixed: Customized question containing an error could cause a crash
• Fixed: Feedback tool detects Windows 10 properly
• Fixed: Mouse cursor when drag-dropping a question
• Fixed: Keyboard shortcut for changing order of question sets in assignment

## Included in version 2.15 released 7/14/2016:

• Improved: Reorder question sets by dragging and dropping
• Improved: Move individual questions within a set by dragging and dropping
• Improved: Presentation View - Commands now on a movable, dockable toolbar
• Improved: Added option for large toolbar icons
• Improved: New icons
• Fixed: Certain options could result in double parenthesis or parenthesis around a negative sign
• Fixed: Arrow over vector variable name not red when appropriate
• Fixed: Solving Systems of Equations by Graphing - Answer could be displayed twice
• Fixed: Equations of Parabolas - Certain givens indicate wrong sign

## Included in version 2.11 released 5/13/2016:

• Improved: [Windows] "Export to clipboard as bitmap" pastes into Microsoft Word at appropriate DPI
• Fixed: Keyboard shortcut for adding space to question set

## Included in version 2.10 released 5/11/2016:

• New: Preference for including "None of the above" as a choice
• New: One column layout
• New: Added support for Infinite Precalculus
• New: Easily add piecewise functions of graphs in custom questions: Example: piecewise([2x-3] if [x<5], [x-1] if [x >= 5])
• New: Easily add functions with restricted domains to graphs in custom questions Example: function(x/2, x<0)
• Improved: More efficient layout of choices
• Improved: [Mac] Added option for legal paper in page setup
• Fixed: Spelling and grammatical errors
• Fixed: Graphing Quadratic Functions - Prevent equivalent choices
• Fixed: Binomial Theorem - Certain options didn't allow for many questions
• Fixed: Right Triangle Trig - Couldn't select just one ratio except sine
• Fixed: Right Triangle Trig - Answer sometimes given in problem
• Fixed: Law of Cosines - Certain SAS cases could freeze program
• Note: Older versions will not be able to open assignments saved with this version

## Included in version 2.06 released 8/3/2015:

• Fixed: Crash when saving if previously used folder no longer exists

## Included in version 2.05 released 7/20/2015:

• New Topic: Sample Spaces and The Fundamental Counting Principle
• New Topic: Independent and Dependent Events
• New Topic: Independent and Dependent Events Word Problems
• New Topic: Mutually Exclusive Events
• New Topic: Mutually Exclusive Events Word Problems
• Fixed: Classifying Conics - Checkboxes for conic types had no effect
• Fixed: Presentation View - Displayed wrong directions in 3-up mode
• Fixed: Presentation View - Lines too long after creating new problems
• Fixed: [Windows] Uncommon error when using the network

## Included in version 2.04.40 released 3/31/2015:

• Fixed: Activation data unrecognized under special circumstances
• Fixed: [Windows] Help files broken by previous release
• Fixed: Order of Operations - Radio buttons reversed

## Included in version 2.04.20 released 3/23/2015:

• Improved: [Windows] "Export to clipboard as bitmap" uses a transparent background

## Included in version 2.04 released 3/17/2015:

• New Topic: Permutations
• New Topic: Combinations
• New Topic: Permutations vs Combinations
• New Topic: Probability with Permutations and Combinations
• New Topic: Converting Degrees and Degrees-Minutes-Seconds
• [factorial(n)]
• [perm(n, r)]
• [comb(n, r)]
• Improved: Better support for proxies
• Improved: Support for HiDPI Mac Retina displays
• Improved: Print options window - Some settings are now persistent
• Improved: Presentation View - Use arrow keys to navigate between questions
• Improved: Question set updates free response/multiple-choice when all questions have changed
• Improved: [Mac] Activation also checks /Library/Preferences/ks-config.txt for serial numbers
• Fixed: [Windows] Crash when printing with certain printers
• Fixed: Crash when loading an assignment with over 80 custom questions
• Fixed: Custom question answer was never choice A
• Fixed: Paper size set before printing
• Fixed: Cramer's Rule - Fixed directions
• Fixed: Systems of Three Equations - Restored the option to "only solve for x"
• Fixed: Center of circle wasn't appearing

## Included in version 2.03 released 9/19/2014:

• Fixed: Preference for question layout mode not correctly loaded
• Fixed: Issues with automatic spacing and highlighting questions when using tight layout
• Fixed: In Presentation View, graphing problems display choices more compactly
• Fixed: Printing blank pages on HP LaserJet 1018, 1020, and 1022 among others
• Fixed: Logs and Exponents as Inverses - problem with slider

## Included in version 2.02 released 8/5/2014:

• New: Software uses system proxy when necessary
• Improved: Activation window has taskbar entry
• Improved: Remembers the last directory used when saving and opening files
• Fixed: [Windows only] Possible crash when loading an assignment with a lot of custom questions
• Fixed: [Mac only] Application stops responding to hover events
• Fixed: Activation from before v2.0 sometimes not recognized
• Fixed: Export to clipboard sometimes cuts off choices B and D
• Fixed: Help contents could become unusable
• Fixed: Word wrap when modifying a question
• Fixed: Memory leak

## Included in version 2.01 released 7/28/2014:

• Fixed: Could crash when opening an assignment from a different program

## Included in version 2.00 released 7/23/2014:

• New: Print to PDF
• New: Filter for topic list
• New: Zoom while viewing on screen
• New: "More like these" button in presentation mode
• New: Show where punch holes will go on the page
• New: Print only an answer sheet
• New: When printing, page range is enabled
• New: Page elements are outlined when hovered
• New: Double-click on directions to change them
• New: When merging assignments, options to put similar topics together or put them end-to-end
• New: Highlight and go to the questions in a question set (menu command or shift-click)
• New: Site licenses can be activated per-machine if run by the administrator
• Ctrl-Click on a question
• Shift-Click on a question
• Ctrl-Shift-Click on a question
• Shift-Click in a empty area of a page
• Ctrl-Shift-Click in a empty area of a page
• Shift-Click on a question set
• Ctrl-Shift-Click on a question set
• Improved: Assignment files are drastically smaller
• Improved: Sidebar is dockable on either side, can be floated, and position reset
• Improved: Auto-spacing doesn't leave dead space at bottom of each page
• Improved: Preview when editing directions
• Improved: Keyboard shortcuts work no matter where the focus is
• Improved: Scale number of questions window more user-friendly
• Fixed: Minor bugs in seven topics

## Included in version 1.56 released 8/14/2013:

• Fixed: Graphing Exponential Functions - Correct choice used lighter shade of blue
• Fixed: Radical Equations could be missing a solution
• Fixed: Graphs of Polynomial Functions - Inflection points sometimes listed as local extrema
• Fixed: Properties of Exponents - Occasionally answer wasn't fully simplified
• Fixed: Dividing Polynomials - Occasionally polynomial was evenly divisible when it shouldn't have been
• Fixed: Graphing Rational Functions - Minor UI issue
• Fixed: Geometric Sequences - Given information sometimes allowed for two possible common ratios
• Fixed: Dividing Polynomials could freeze
• Fixed: Systems of Equations by Elimination - "No solution" occasionally should have been "Infinite solutions"

## Included in version 1.55 released 12/11/2012:

• New: Graphs can be added to custom questions
• Improved: Graphing and Graph Paper utility more powerful and easier to use
• Fixed: Choices for Evaluating Functions with a variable operand could contain wrong variable
• Fixed: Choices for Function Operations with a variable operand could contain wrong variable
• Fixed: Function Operations, functions when composed with self could provide the wrong answer
• Fixed: Custom questions with an illegal expression could freeze the program
• Fixed: Certain families of functions graphed incorrectly

## Included in version 1.53 released 9/11/2012:

• New: Preference for notation for greatest integer function
• New: Added maximize/restore button to Presentation View
• New: Graphing Absolute Value Equations has options for including coefficients
• Improved: Help files
• Improved: Scroll bars
• Improved: User interface
• Improved: When choices make a question too tall for a page, some choices are removed
• Improved: Algebraic simplification routines are now more efficient
• Improved: Better graphs for: Graphing Absolute Value Equations, Graphing Linear Equations, Graphing Exponential Functions, Graphing Quadratic Functions, Graphing Linear Inequalities, Graphing Systems of Linear Inequalities
• Improved: Better number lines for: Multi-Step Inequalities, Compound Inequalities, Absolute Value Inequalities
• Fixed: Wrapping to full-page and half-page could be too wide
• Fixed: Able to graph certain families of functions
• Fixed: Graphs for Compound Inequalities could omit interval
• Fixed: Double & Half Angle Identities: Button to show more examples did not work
• Fixed: Writing Linear Equations: Answer can't be line given in question

## Included in version 1.52 released 5/29/2012:

• Improved: More professional radical signs
• Improved: Graphs of discontinuous functions have breaks and open / closed holes
• Improved: Even less likely to crash when generating questions
• Fixed: Word wrapping could skip blank lines, not wrap where appropriate
• Fixed: Wrapping to full page in a custom question was too wide
• Fixed: Products of powers of e (like 2 e &sup3;) no longer display with a multiplication dot
• Fixed: Most diagrams appeared incorrectly in print preview
• Fixed: Random error message on save or load
• Fixed: Graphing Rational Functions: Open holes in graph could appear as filled holes

## Included in version 1.51.02 released on 4/9/2012:

• Fixed: Minimum Windows version was set incorrectly

## Included in version 1.51 released 4/5/2012:

• New: Added greatest integer function / floor function to custom questions    Example: Find [int(2x)] when [x=3/5]
• New: Added piecewise functions to custom questions    Example: [eval(f,x)] = [piecewise [x] if [x < 0], [xx] if [x >= 0]]
• Improved: Faster! Optimized rendering of questions to screen
• Improved: Faster! Optimized graphing routines
• Improved: Improved graphing capabilities
• Improved: Diagrams drawn more smoothly on screen
• Fixed: Graphs could omit holes
• Fixed: Graphs of constant functions or those involving e and π could be incorrect
• Fixed: Minor indentation issue in custom questions
• Fixed: Horizontal asymptotes could be drawn beyond a graph's area

## Included in version 1.50 released 3/15/2012:

• New: Presentation View window is resizeable
• New: Presentation View has option to automatically hide the answers when a new question is displayed
• New: High-level filter to prevent questions from containing an illegal expression
• Improved: Function notation can now be edited
• Improved: Faster! Optimized the simplification of mathematical expressions
• Improved: Faster! Improved undo/redo algorithm
• Improved: Smaller executable size
• Improved: "Current Question Sets" list easier to use
• Improved: Options windows resize more smoothly
• Fixed: Equation of Parabolas could freeze
• Fixed: Geometric Series questions could list "Illegal Expression" as a choice
• Fixed: Graphing Exponential Functions could freeze
• Fixed: Systems of Equations Word Problems could freeze
• Fixed: Punctuation in some word problems
• Fixed: Certain expressions in a custom question would cause the software to crash
• Fixed: Expressions like root × term would not print a multiplication dot
• Note: Beginning with this version, Windows XP SP3 is the minimum required version of Windows

## Included in version 1.45 released 4/12/2011:

• New: Assignments from this program can be opened and modified by our other programs          (Assignments saved with v1.45 or greater can be opened by other programs v1.45 or greater)
• New: Student data fields (name, date, period) can be renamed
• New: Additional student data field available
• New: Add & Continue is available when modifying an existing question set
• New: Link to this details page when a software update is available
• New: Product serial numbers can be placed in config.txt to facilitate enterprise installations
• Improved: Better backwards- and future-compatibility
• Fixed: Assignments with quotes in the title don't prevent Save As
• Fixed: Quotients could be sometimes be simplified incorrectly
• Fixed: Choices for dilations sometimes inappropriate
• Fixed: Dilations rounding x- and y-coordinates
• Fixed: Function Operations could have "Illegal Expression" as an answer or as a choice
• Fixed: Multi-Step Equations: Program could freeze
• Fixed: Dividing Radical Expressions: Program could freeze
• Fixed: Add & Continue respects change in problem type
• Fixed: Powers of i are correctly displayed

## Included in version 1.42 released on 6/28/2010:

• New: Automatically checks for updates
• New: List topics by index order or suggested order

## Included in version 1.40 released 2/8/2010:

• New Preference: 'Spacious' or 'tight' layout of questions on page
• Improved: Question sets with one question are more intelligently spaced
• Improved: Graphs with small ranges now look better
• Improved: Options screen now resizeable
• Fixed: Directions occasionally orphaned at bottom of page
• Fixed: Correct numbers changed because zeros at the end of a number were deleted (50 --> 5)

## Included in version 1.08.20 released 5/22/2009:

• Changed: Minor change to license agreement so that renewals extend the termination date instead of beginning a new term.

## Included in version 1.08 released 4/10/2009:

• New: Possible to change directions for a set without regenerating questions
• Improved: Changing directions cascades changes to appropriate neighbors
• Correction: Answers to Properties of Exponents could have wrong sign
• Correction: Inequalities were sometimes solved incorrectly
• Fixed: Software sometimes failed to renumber questions in assignment

## Included in version 1.07 released 1/6/2009:

• New: Trig. equations that don't require factoring
• Correction: Function operations / linear combinations answers sometimes wrong
• Fixed: Software crashes when starting if closed when side panel is minimized

## Included in version 1.06 released 12/4/2008:

• Improved: Isolate up to four questions on screen at once
• Improved: Support for computers with multiple processors
• Improved: User interface: Toolbar + Preferences
• Fixed: Obscure error involving selecting a question and scaling the assignment

## Included in version 1.03 released 10/1/2008:

• New: Export individual questions as bitmaps
• Improved: Custom questions wrap to whole/half page
• Improved: Insert special symbols and math in custom questions
• Improved: Insert 'blanks' into math text
• Improved: Line thickness preference also now controls darkness of grid lines in graphs
• Correction: Writing logs in terms of others sometimes created duplicate questions
• Fixed: Internet calls would sometimes report wrong error

## Included in version 1.02 released 9/18/2008:

• Correction: Question type was not saving all of its options
• Correction: Equations of Hyperbolas description was sometimes wrong
• Correction: Geometric Series directions was sometimes wrong
• Correction: Binomial Theorem type could cause the program to freeze
• Correction: Rational Exponents answers now correct
• Fixed: Internet calls could freeze program

## Try Infinite Algebra 2 Today!

Discover the power and flexibility of our software firsthand with a free, 14-day trial. Installation is fast and simple. Within minutes, you can have the software installed and create the precise worksheets you need -- even for today's lesson.

Use each trial for up to 14 days. The trial version is identical to the retail version except that you cannot print to electronic formats such as PDF.

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## 1.20: Word Problems for Linear Equations

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• Page ID 45640

Word problems are important applications of linear equations. We start with examples of translating an English sentence or phrase into an algebraic expression.

Example 18.1

Translate the phrase into an algebraic expression:

a) Twice a variable is added to 4

Solution: We call the variable $$x .$$ Twice the variable is $$2 x .$$ Adding $$2 x$$ to 4 gives:

$4 + 2x\nonumber$

b) Three times a number is subtracted from 7.

Solution: Three times a number is $$3 x .$$ We need to subtract $$3 x$$ from 7. This means:\

$7-3 x\nonumber$

c) 8 less than a number.

Solution: The number is denoted by $$x .8$$ less than $$x$$ mean, that we need to subtract 8 from it. We get:

$x-8\nonumber$

For example, 8 less than 10 is $$10-8=2$$.

d) Subtract $$5 p^{2}-7 p+2$$ from $$3 p^{2}+4 p$$ and simplify.

Solution: We need to calculate $$3 p^{2}+4 p$$ minus $$5 p^{2}-7 p+2:$$

$\left(3 p^{2}+4 p\right)-\left(5 p^{2}-7 p+2\right)\nonumber$

Simplifying this expression gives:

$\left(3 p^{2}+4 p\right)-\left(5 p^{2}-7 p+2\right)=3 p^{2}+4 p-5 p^{2}+7 p-2 =-2 p^{2}+11 p-2\nonumber$

e) The amount of money given by $$x$$ dimes and $$y$$ quarters.

Solution: Each dime is worth 10 cents, so that this gives a total of $$10 x$$ cents. Each quarter is worth 25 cents, so that this gives a total of $$25 y$$ cents. Adding the two amounts gives a total of

$10 x+25 y \text{ cents or } .10x + .25y \text{ dollars}\nonumber$

Now we deal with word problems that directly describe an equation involving one variable, which we can then solve.

Example 18.2

Solve the following word problems:

a) Five times an unknown number is equal to 60. Find the number.

Solution: We translate the problem to algebra:

$5x = 60\nonumber$

We solve this for $$x$$ :

$x=\frac{60}{5}=12\nonumber$

b) If 5 is subtracted from twice an unknown number, the difference is $$13 .$$ Find the number.

Solution: Translating the problem into an algebraic equation gives:

$2x − 5 = 13\nonumber$

We solve this for $$x$$. First, add 5 to both sides.

$2x = 13 + 5, \text{ so that } 2x = 18\nonumber$

Dividing by 2 gives $$x=\frac{18}{2}=9$$.

c) A number subtracted from 9 is equal to 2 times the number. Find the number.

Solution: We translate the problem to algebra.

$9 − x = 2x\nonumber$

We solve this as follows. First, add $$x$$ :

$9 = 2x + x \text{ so that } 9 = 3x\nonumber$

Then the answer is $$x=\frac{9}{3}=3$$

d) Multiply an unknown number by five is equal to adding twelve to the unknown number. Find the number.

Solution: We have the equation:

$5x = x + 12.\nonumber$

Subtracting $$x$$ gives

$4x = 12.\nonumber$

Dividing both sides by 4 gives the answer: $$x=3$$.

e) Adding nine to a number gives the same result as subtracting seven from three times the number. Find the number.

Solution: Adding 9 to a number is written as $$x+9,$$ while subtracting 7 from three times the number is written as $$3 x-7$$. We therefore get the equation:

$x + 9 = 3x − 7.\nonumber$

We solve for $$x$$ by adding 7 on both sides of the equation:

$x + 16 = 3x.\nonumber$

Then we subtract $$x:$$

$16 = 2x.\nonumber$

After dividing by $$2,$$ we obtain the answer $$x=8$$

The following word problems consider real world applications. They require to model a given situation in the form of an equation.

Example 18.3

a) Due to inflation, the price of a loaf of bread has increased by $$5 \%$$. How much does the loaf of bread cost now, when its price was $$\ 2.40$$ last year?

Solution: We calculate the price increase as $$5 \% \cdot \ 2.40 .$$ We have

$5 \% \cdot 2.40=0.05 \cdot 2.40=0.1200=0.12\nonumber$

We must add the price increase to the old price.

$2.40+0.12=2.52\nonumber$

The new price is therefore $$\ 2.52$$.

b) To complete a job, three workers get paid at a rate of $$\ 12$$ per hour. If the total pay for the job was $$\ 180,$$ then how many hours did the three workers spend on the job?

Solution: We denote the number of hours by $$x$$. Then the total price is calculated as the price per hour $$(\ 12)$$ times the number of workers times the number of hours $$(3) .$$ We obtain the equation

$12 \cdot 3 \cdot x=180\nonumber$

Simplifying this yields

$36 x=180\nonumber$

Dividing by 36 gives

$x=\frac{180}{36}=5\nonumber$

Therefore, the three workers needed 5 hours for the job.

c) A farmer cuts a 300 foot fence into two pieces of different sizes. The longer piece should be four times as long as the shorter piece. How long are the two pieces?

$x+4 x=300\nonumber$

Combining the like terms on the left, we get

$5 x=300\nonumber$

Dividing by 5, we obtain that

$x=\frac{300}{5}=60\nonumber$

Therefore, the shorter piece has a length of 60 feet, while the longer piece has four times this length, that is $$4 \times 60$$ feet $$=240$$ feet.

d) If 4 blocks weigh 28 ounces, how many blocks weigh 70 ounces?

Solution: We denote the weight of a block by $$x .$$ If 4 blocks weigh $$28,$$ then a block weighs $$x=\frac{28}{4}=7$$

How many blocks weigh $$70 ?$$ Well, we only need to find $$\frac{70}{7}=10 .$$ So, the answer is $$10 .$$

Note You can solve this problem by setting up and solving the fractional equation $$\frac{28}{4}=\frac{70}{x}$$. Solving such equations is addressed in chapter 24.

e) If a rectangle has a length that is three more than twice the width and the perimeter is 20 in, what are the dimensions of the rectangle?

Solution: We denote the width by $$x$$. Then the length is $$2 x+3$$. The perimeter is 20 in on one hand and $$2($$length$$)+2($$width$$)$$ on the other. So we have

$20=2 x+2(2 x+3)\nonumber$

Distributing and collecting like terms give

$20=6 x+6\nonumber$

Subtracting 6 from both sides of the equation and then dividing both sides of the resulting equation by 6 gives:

$20-6=6 x \Longrightarrow 14=6 x \Longrightarrow x=\frac{14}{6} \text { in }=\frac{7}{3} \text { in }=2 \frac{1}{3} \text { in. }\nonumber$

f) If a circle has circumference 4in, what is its radius?

Solution: We know that $$C=2 \pi r$$ where $$C$$ is the circumference and $$r$$ is the radius. So in this case

$4=2 \pi r\nonumber$

Dividing both sides by $$2 \pi$$ gives

$r=\frac{4}{2 \pi}=\frac{2}{\pi} \text { in } \approx 0.63 \mathrm{in}\nonumber$

g) The perimeter of an equilateral triangle is 60 meters. How long is each side?

Solution: Let $$x$$ equal the side of the triangle. Then the perimeter is, on the one hand, $$60,$$ and on other hand $$3 x .$$ So $$3 x=60$$ and dividing both sides of the equation by 3 gives $$x=20$$ meters.

h) If a gardener has $$\ 600$$ to spend on a fence which costs $$\ 10$$ per linear foot and the area to be fenced in is rectangular and should be twice as long as it is wide, what are the dimensions of the largest fenced in area?

Solution: The perimeter of a rectangle is $$P=2 L+2 W$$. Let $$x$$ be the width of the rectangle. Then the length is $$2 x .$$ The perimeter is $$P=2(2 x)+2 x=6 x$$. The largest perimeter is $$\ 600 /(\ 10 / f t)=60$$ ft. So $$60=6 x$$ and dividing both sides by 6 gives $$x=60 / 6=10$$. So the dimensions are 10 feet by 20 feet.

i) A trapezoid has an area of 20.2 square inches with one base measuring 3.2 in and the height of 4 in. Find the length of the other base.

Solution: Let $$b$$ be the length of the unknown base. The area of the trapezoid is on the one hand 20.2 square inches. On the other hand it is $$\frac{1}{2}(3.2+b) \cdot 4=$$ $$6.4+2 b .$$ So

$20.2=6.4+2 b\nonumber$

Multiplying both sides by 10 gives

$202=64+20 b\nonumber$

Subtracting 64 from both sides gives

$b=\frac{138}{20}=\frac{69}{10}=6.9 \text { in }\nonumber$

and dividing by 20 gives

Exit Problem

Write an equation and solve: A car uses 12 gallons of gas to travel 100 miles. How many gallons would be needed to travel 450 miles?

## Linear Equation Word Problems - Examples & Practice - Expii

Linear equation word problems - examples & practice, explanations (3), (video) slope-intercept word problems.

by cpfaffinator

This video by cpfaffinator explains how to translate word problems into variables while working through a couple of examples.

(Note: the answer at 3:34 should be y=0.50x+3 instead of y=0.5x+b .)

When writing linear equations (also called linear models) from word problems, you need to know what the x and y variables refer to, as well as what the slope and y-intercept are. Here are some tricks to help translate :

• The x variable. Usually, you'll be asked to find an equation in terms of some factor. This will usually be whatever affects the output of the equation.
• The y variable. The y variable is usually whatever you're trying to find in the problem. It'll depend on the x variable.
• The slope (m). The slope will be some sort of rate or other change over time.
• The y-intercept (b). Look for a starting point or extra fees—something that will be added (or subtracted) on , no matter what the x variable is.

Using these parts, we can write the word problem in slope intercept form , y=mx+b, and solve.

A city parking garage charges a flat rate of $3.00 for parking 2 hours or less, and$0.50 per hour for each additional hour. Write a linear model that gives the total charge in terms of additional hours parked.

First up, we want the equation, or model, to give us the total charge. This will be what the y variable represents. y=total charge for parking The total charge depends on how many additional hours you've parked. This is the x variables. x=additional hours parked

Next, we need to find the slope, m. If we look at the slope-intercept equation , y=mx+b, the slope is multiplied with the input x. So, we want to find some rate in our problem that goes with the number of additional hours parked . In the problem, we have $0.50 per hour for each additional hour. The number of hours is being multiplied by the price of 50 cents every hour. m=0.50 The y-intercept is the starting point. In other words, if we parked our car in the garage for 0 hours, what would the price be? The problem says the garage *charges a flat rate of$3.00. A flat rate means that no matter what we're being charged 3 dollars. b=3

Plugging these into the slope-intercept equation will give us our model. y=mx+by=0.50x+3

Six 2 foot tall pine trees were planted during the school's observation of Earth Awareness Week in 1990. The trees have grown at an average rate of 34 foot per year. Write a linear model that gives the height of the trees in terms of the number of years since they were planted.

What does the y variable represent in our equation?

Years since the trees were planted

Number of trees planted

Height of the trees

## Related Lessons

Translate to a linear equation.

Sometimes, the trick to solving a word problem will be to translate it into a linear equation. To clue you in, linear equation word problems usually involve some sort of rate of change , or steady increase (or decrease) based on a single variable. If you see the word rate , or even "per" or "each" , it's a safe bet that a word problem is calling for a linear equation.

There are a couple steps when translating from a word problem to a linear equation. Review them, then we'll work through an example.

• Find the y variable, or output. What is the thing you're trying to find? This will often be a price, or an amount of time, or something else countable that depends on other things.
• Find the x variable, or input. What is affecting the price, or amount of time, etc.?
• Find the slope. What's the rate in the problem?
• Find the y-intercept. Is there anything that's added or subtracted on top of the rate, no matter what what x is?
• Plug all the numbers you know into y=mx+b !
Wally and Cobb are starting a catering business. They rent a kitchen for $350 a month, and charge$75 for each event they cater. If they cater 12 events in a month, how much do they profit?

First, let's find the y variable. What are we trying to find in this problem?

## Word Problems with Linear Relationships

When you're faced with a linear word problem, it can feel daunting to work out a solution. The good news is that there are few simple steps that you can take to tackle linear word problems.

Image source: by Anusha Rahman

For future linear word problems, you can use these same steps to tackle the problem!

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## Course: Algebra 1   >   Unit 5

• Intro to slope-intercept form
• Slope and y-intercept from equation
• Worked examples: slope-intercept intro
• Slope-intercept intro
• Linear equation word problems

## Linear equations word problems

• an integer, like 6 ‍
• a simplified proper fraction, like 3 / 5 ‍
• a simplified improper fraction, like 7 / 4 ‍
• a mixed number, like 1   3 / 4 ‍
• an exact decimal, like 0.75 ‍
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍

## Word Problems Linear Equations

Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

## $$\textbf{1)}$$ Joe and Steve are saving money. Joe starts with $105 and saves$5 per week. Steve starts with $5 and saves$15 per week. After how many weeks do they have the same amount of money? Show Equations $$y= 5x+105,\,\,\,y=15x+5$$ Show Answer 10 weeks ($155) $$\textbf{2)}$$ mike and sarah collect rocks. together they collected 50 rocks. mike collected 10 more rocks than sarah. how many rocks did each of them collect show equations $$m+s=50,\,\,\,m=s+10$$ show answer mike collected 30 rocks, sarah collected 20 rocks., $$\textbf{3)}$$ in a classroom the ratio of boys to girls is 2:3. there are 25 students in the class. how many are girls show equations $$b+g=50,\,\,\,3b=2g$$ show answer 15 girls (10 boys), $$\textbf{4)}$$ kyle makes sandals at home. the sandal making tools cost$100 and he spends $10 on materials for each sandal. he sells each sandal for$30. how many sandals does he have to sell to break even show equations $$c=10x+100,\,\,\,r=30x$$ show answer 5 sandals ($150), $$\textbf{5)}$$ molly is throwing a beach party. she still needs to buy beach towels and beach balls. towels are$3 each and beachballs are $4 each. she bought 10 items in total and it cost$34. how many beach balls did she get show equations show answer 4 beachballs (6 towels), $$\textbf{6)}$$ anna volunteers at a pet shelter. they have cats and dogs. there are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. how many cats are at the shelter show equations $$c+d=40,\,\,\,5d=4c$$ show answer 20 cats (16 dogs), $$\textbf{7)}$$ a store sells oranges and apples. oranges cost $1.00 each and apples cost$2.00 each. in the first sale of the day, 15 fruits were sold in total, and the price was $25. how many of each type of frust was sold show equations $$o+a=15,\,\,\,1o+2a=25$$ show answer 10 apples and 5 oranges, $$\textbf{8)}$$ the ratio of red marbles to green marbles is 2:7. there are 36 marbles in total. how many are red show equations $$r+g=36,\,\,\,7r=2g$$ show answer 8 red marbles (28 green marbles), $$\textbf{9)}$$ a tennis club charges$100 to join the club and $10 for every hour using the courts. write an equation to express the cost $$c$$ in terms of $$h$$ hours playing tennis. show equation the equation is $$c=10h+100$$, $$\textbf{10)}$$ emma and liam are saving money. emma starts with$80 and saves $10 per week. liam starts with$120 and saves $6 per week. after how many weeks will they have the same amount of money show equations $$e = 10x + 80,\,\,\,l = 6x + 120$$ show answer 10 weeks ($180 each), $$\textbf{11)}$$ mark and lisa collect stamps. together they collected 200 stamps. mark collected 40 more stamps than lisa. how many stamps did each of them collect show equations $$m + l = 200,\,\,\,m = l + 40$$ show answer mark collected 120 stamps, lisa collected 80 stamps., $$\textbf{12)}$$ in a classroom, the ratio of boys to girls is 3:5. there are 40 students in the class. how many are boys show equations $$b + g = 40,\,\,\,5b = 3g$$ show answer 15 boys (25 girls), $$\textbf{13)}$$ lisa is selling handmade jewelry. the materials cost $60, and she sells each piece for$20. how many pieces does she have to sell to break even show equations $$c=60,\,\,\,r=20x$$ show answer 3 pieces, $$\textbf{14)}$$ tom is buying books and notebooks for school. books cost $15 each, and notebooks cost$3 each. he bought 12 items in total, and it cost $120. how many notebooks did he buy show equations $$b + n = 12,\,\,\,15b+3n=120$$ show answer 5 notebooks (7 books), $$\textbf{15)}$$ emily volunteers at an animal shelter. they have rabbits and guinea pigs. there are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. how many guinea pigs are at the shelter show equations $$r + g = 36,\,\,\,5g=4r$$ show answer 16 guinea pigs (20 rabbits), $$\textbf{16)}$$ mike and sarah are going to a theme park. mike’s ticket costs$40, and sarah’s ticket costs $30. they also bought$20 worth of food. how much did they spend in total show equations $$m + s + f = t,\,\,\,m=40,\,\,\,s=30,\,\,\,f=20$$ show answer they spent $90 in total., $$\textbf{17)}$$ the ratio of red marbles to blue marbles is 2:3. there are 50 marbles in total. how many are blue show equations $$r + b = 50,\,\,\,3r=2b$$ show answer 30 blue marbles (20 red marbles), $$\textbf{18)}$$ a pizza restaurant charges$12 for a large pizza and $8 for a small pizza. if a customer buys 5 pizzas in total, and it costs$52, how many large pizzas did they buy show equations $$l + s = 5,\,\,\,12l+8s=52$$ show answer they bought 3 large pizzas (2 small pizzas)., $$\textbf{19)}$$ the area of a rectangle is 48 square meters. if the length is 8 meters, what is the width of the rectangle show equations $$a=l\times w,\,\,\,l=8,\,\,\,a=48$$ show answer the width is 6 meters., $$\textbf{20)}$$ two numbers have a sum of 50. one number is 10 more than the other. what are the two numbers show equations $$x+y=50,\,\,\,x=y+10$$ show answer the numbers are 30 and 20., $$\textbf{21)}$$ a store sells jeans for $40 each and t-shirts for$20 each. in the first sale of the day, they sold 8 items in total, and the price was $260. how many of each type of item was sold show equations $$j+t=8,\,\,\,40j+20t=260$$ show answer 5 jeans and 3 t-shirts were sold., $$\textbf{22)}$$ the ratio of apples to carrots is 3:4. there are 28 fruits in total. how many are apples show equations a+c=28,\,\,\,4a=3c show answer there are 12 apples and 16 carrots., $$\textbf{23)}$$ a phone plan costs$30 per month, and there is an additional charge of $0.10 per minute for calls. write an equation to express the cost $$c$$ in terms of $$m$$ minutes. show equation the equation is c=30+0.10m, $$\textbf{24)}$$ a triangle has a base of 8 inches and a height of 6 inches. calculate its area. show equations $$a=0.5\times b\times h,\,\,\,b=8,\,\,\,h=6$$ show answer the area is 24 square inches., $$\textbf{25)}$$ a store sells shirts for$25 each and pants for $45 each. in the first sale of the day, 4 items were sold, and the price was$180. how many of each type of item was sold show equations $$t+p=4,\,\,\,25t+45p=180$$ show answer 0 shirts and 4 pants were sold., $$\textbf{26)}$$ a garden has a length of 12 feet and a width of 10 feet. calculate its area. show equations $$a=l\times w,\,\,\,l=12,\,\,\,w=10$$ show answer the area is 120 square feet., $$\textbf{27)}$$ the sum of two consecutive odd numbers is 56. what are the two numbers show equations $$x+y=56,\,\,\,x=y+2$$ show answer the numbers are 27 and 29., $$\textbf{28)}$$ a toy store sells action figures for $15 each and toy cars for$5 each. in the first sale of the day, 10 items were sold, and the price was $110. how many of each type of item was sold show equations $$a+c=10,\,\,\,15a+5c=110$$ show answer 6 action figures and 4 toy cars were sold., $$\textbf{29)}$$ a bakery sells pie for$2 each and cookies for $1 each. in the first sale of the day, 14 items were sold, and the price was$25. how many of each type of item was sold show equations $$p+c=14,\,\,\,2p+c=25$$ show answer 11 pies and 3 cookies were sold., $$\textbf{for 30-33}$$ two car rental companies charge the following values for x miles. car rental a: $$y=3x+150 \,\,$$ car rental b: $$y=4x+100$$, $$\textbf{30)}$$ which rental company has a higher initial fee show answer company a has a higher initial fee, $$\textbf{31)}$$ which rental company has a higher mileage fee show answer company b has a higher mileage fee, $$\textbf{32)}$$ for how many driven miles is the cost of the two companies the same show answer the companies cost the same if you drive 50 miles., $$\textbf{33)}$$ what does the $$3$$ mean in the equation for company a show answer for company a, the cost increases by $3 per mile driven., $$\textbf{34)}$$ what does the $$100$$ mean in the equation for company b show answer for company b, the initial cost (0 miles driven) is$100., $$\textbf{for 35-39}$$ andy is going to go for a drive. the formula below tells how many gallons of gas he has in his car after m miles. $$g=12-\frac{m}{18}$$, $$\textbf{35)}$$ what does the $$12$$ in the equation represent show answer andy has $$12$$ gallons in his car when he starts his drive., $$\textbf{36)}$$ what does the $$18$$ in the equation represent show answer it takes $$18$$ miles to use up $$1$$ gallon of gas., $$\textbf{37)}$$ how many miles until he runs out of gas show answer the answer is $$216$$ miles, $$\textbf{38)}$$ how many gallons of gas does he have after 90 miles show answer the answer is $$7$$ gallons, $$\textbf{39)}$$ when he has $$3$$ gallons remaining, how far has he driven show answer the answer is $$162$$ miles, $$\textbf{for 40-42}$$ joe sells paintings. each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest., $$\textbf{40)}$$ find the equation of how much money x joe needs to sell to earn y dollars per month. show answer the answer is $$y=.1(x-5,000)$$, $$\textbf{41)}$$ how much does joe need to sell to earn$10,000 in a month. show answer the answer is $$105,000$$, $$\textbf{42)}$$ how much does joe earn if he sells $45,000 in a month show answer the answer is $$4,000$$, see related pages, $$\bullet\text{ word problems- linear equations}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- averages}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- consecutive integers}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- distance, rate and time}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- break even}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- ratios}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- age}$$ $$\,\,\,\,\,\,\,\,$$, $$\bullet\text{ word problems- mixtures and concentration}$$ $$\,\,\,\,\,\,\,\,$$, linear equations are a type of equation that has a linear relationship between two variables, and they can often be used to solve word problems. in order to solve a word problem involving a linear equation, you will need to identify the variables in the problem and determine the relationship between them. this usually involves setting up an equation (or equations) using the given information and then solving for the unknown variables . linear equations are commonly used in real-life situations to model and analyze relationships between different quantities. for example, you might use a linear equation to model the relationship between the cost of a product and the number of units sold, or the relationship between the distance traveled and the time it takes to travel that distance. linear equations are typically covered in a high school algebra class. these types of problems can be challenging for students who are new to algebra, but they are an important foundation for more advanced math concepts. one common mistake that students make when solving word problems involving linear equations is failing to set up the problem correctly. it’s important to carefully read the problem and identify all of the relevant information, as well as any given equations or formulas that you might need to use. other related topics involving linear equations include graphing and solving systems. understanding linear equations is also useful for applications in fields such as economics, engineering, and physics., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting. ## Word Problems on Linear Equations Worked-out word problems on linear equations with solutions explained step-by-step in different types of examples. There are several problems which involve relations among known and unknown numbers and can be put in the form of equations. The equations are generally stated in words and it is for this reason we refer to these problems as word problems. With the help of equations in one variable, we have already practiced equations to solve some real life problems. Steps involved in solving a linear equation word problem: ● Read the problem carefully and note what is given and what is required and what is given. ● Denote the unknown by the variables as x, y, ……. ● Translate the problem to the language of mathematics or mathematical statements. ● Form the linear equation in one variable using the conditions given in the problems. ● Solve the equation for the unknown. ● Verify to be sure whether the answer satisfies the conditions of the problem. ## Step-by-step application of linear equations to solve practical word problems: 1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers. Solution: Then the other number = x + 9 Let the number be x. Sum of two numbers = 25 According to question, x + x + 9 = 25 ⇒ 2x + 9 = 25 ⇒ 2x = 25 - 9 (transposing 9 to the R.H.S changes to -9) ⇒ 2x = 16 ⇒ 2x/2 = 16/2 (divide by 2 on both the sides) ⇒ x = 8 Therefore, x + 9 = 8 + 9 = 17 Therefore, the two numbers are 8 and 17. 2.The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What are the two numbers? Solution: Let the common ratio be x. Let the common ratio be x. Their difference = 48 According to the question, 7x - 3x = 48 ⇒ 4x = 48 ⇒ x = 48/4 ⇒ x = 12 Therefore, 7x = 7 × 12 = 84 3x = 3 × 12 = 36 Therefore, the two numbers are 84 and 36. 3. The length of a rectangle is twice its breadth. If the perimeter is 72 metre, find the length and breadth of the rectangle. Solution: Let the breadth of the rectangle be x, Then the length of the rectangle = 2x Perimeter of the rectangle = 72 Therefore, according to the question 2(x + 2x) = 72 ⇒ 2 × 3x = 72 ⇒ 6x = 72 ⇒ x = 72/6 ⇒ x = 12 We know, length of the rectangle = 2x = 2 × 12 = 24 Therefore, length of the rectangle is 24 m and breadth of the rectangle is 12 m. 4. Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find their present ages. Solution: Let Ron’s present age be x. Then Aaron’s present age = x - 5 After 4 years Ron’s age = x + 4, Aaron’s age x - 5 + 4. According to the question; Ron will be twice as old as Aaron. Therefore, x + 4 = 2(x - 5 + 4) ⇒ x + 4 = 2(x - 1) ⇒ x + 4 = 2x - 2 ⇒ x + 4 = 2x - 2 ⇒ x - 2x = -2 - 4 ⇒ -x = -6 ⇒ x = 6 Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1 Therefore, present age of Ron = 6 years and present age of Aaron = 1 year. 5. A number is divided into two parts, such that one part is 10 more than the other. If the two parts are in the ratio 5 : 3, find the number and the two parts. Solution: Let one part of the number be x Then the other part of the number = x + 10 The ratio of the two numbers is 5 : 3 Therefore, (x + 10)/x = 5/3 ⇒ 3(x + 10) = 5x ⇒ 3x + 30 = 5x ⇒ 30 = 5x - 3x ⇒ 30 = 2x ⇒ x = 30/2 ⇒ x = 15 Therefore, x + 10 = 15 + 10 = 25 Therefore, the number = 25 + 15 = 40 The two parts are 15 and 25. More solved examples with detailed explanation on the word problems on linear equations. 6. Robert’s father is 4 times as old as Robert. After 5 years, father will be three times as old as Robert. Find their present ages. Solution: Let Robert’s age be x years. Then Robert’s father’s age = 4x After 5 years, Robert’s age = x + 5 Father’s age = 4x + 5 According to the question, 4x + 5 = 3(x + 5) ⇒ 4x + 5 = 3x + 15 ⇒ 4x - 3x = 15 - 5 ⇒ x = 10 ⇒ 4x = 4 × 10 = 40 Robert’s present age is 10 years and that of his father’s age = 40 years. 7. The sum of two consecutive multiples of 5 is 55. Find these multiples. Solution: Let the first multiple of 5 be x. Then the other multiple of 5 will be x + 5 and their sum = 55 Therefore, x + x + 5 = 55 ⇒ 2x + 5 = 55 ⇒ 2x = 55 - 5 ⇒ 2x = 50 ⇒ x = 50/2 ⇒ x = 25 Therefore, the multiples of 5, i.e., x + 5 = 25 + 5 = 30 Therefore, the two consecutive multiples of 5 whose sum is 55 are 25 and 30. 8. The difference in the measures of two complementary angles is 12°. Find the measure of the angles. Solution: Let the angle be x. Complement of x = 90 - x Given their difference = 12° Therefore, (90 - x) - x = 12° ⇒ 90 - 2x = 12 ⇒ -2x = 12 - 90 ⇒ -2x = -78 ⇒ 2x/2 = 78/2 ⇒ x = 39 Therefore, 90 - x = 90 - 39 = 51 Therefore, the two complementary angles are 39° and 51° 9. The cost of two tables and three chairs is$705. If the table costs $40 more than the chair, find the cost of the table and the chair. Solution: The table cost$ 40 more than the chair.  Let us assume the cost of the chair to be x.  Then the cost of the table = $40 + x The cost of 3 chairs = 3 × x = 3x and the cost of 2 tables 2(40 + x) Total cost of 2 tables and 3 chairs =$705 Therefore, 2(40 + x) + 3x = 705 80 + 2x + 3x = 705 80 + 5x = 705 5x = 705 - 80 5x = 625/5 x = 125 and 40 + x = 40 + 125 = 165 Therefore, the cost of each chair is $125 and that of each table is$165.

10. If 3/5 ᵗʰ of a number is 4 more than 1/2 the number, then what is the number?  Solution: Let the number be x, then 3/5 ᵗʰ of the number = 3x/5 Also, 1/2 of the number = x/2  According to the question,  3/5 ᵗʰ of the number is 4 more than 1/2 of the number.  ⇒ 3x/5 - x/2 = 4 ⇒ (6x - 5x)/10 = 4 ⇒ x/10 = 4 ⇒ x = 40 The required number is 40.

Try to follow the methods of solving word problems on linear equations and then observe the detailed instruction on the application of equations to solve the problems.

●   Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

●   Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

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1. PDF Two-Step Word Problems

F Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Two-Step Equation Word Problems Date_____ Period____ 1) 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? 2) Aliyah had $24 to spend on seven pencils. 2. PDF Linear Function Word Problems Infinite Algebra 1 - Linear Function Word Problems Linear Function Word Problems Name___________________________________ ©d l2I0H2\0B [KWuftxac HSgonfvttwsazr_eu WLjLECh.b a lA^lBlW WrmiIgbhXtsu FreeXsOerEvsePdC. Jimmy is having a birthday party at the zoo. The zoo has a fixed fee for birthday parties, plus a fee per person. 3. Free Printable Math Worksheets for Algebra 1 Finding angles of triangles. Finding side lengths of triangles. Statistics. Visualizing data. Center and spread of data. Scatter plots. Using statistical models. Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format. 4. PDF Systems of Equations Word Problems L Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Systems of Equations Word Problems Date_____ Period____ 1) Find the value of two numbers if their sum is 12 and their difference is 4. 4 and 8 2) The difference of two numbers is 3. Their sum is 13. Find the numbers. 5 and 8 5. PDF Kuta Software ©l b2e0 E1R2N gKXuVt4a A LSZoTfmtvwxaVrpe j ELGLsC v.o x PA el hl Y UrviNg2hFt Xs9 8r neosWerUv aeZd h.v 7 aM ra cd ieF sw 6i9tNh7 AIln 7fqi0n1iHtbe H 4P urYeU-KAfl Wgwegbfr PaK.w Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Writing Linear Equations Date_____ Period____ 6. PDF Writing Linear Equations Writing Linear Equations 3) 5) 7) 2) 4) 6) 8) Write the standard form of the equation of the line through the given point with the given slope. 9) through: 11) through: 10) through: 12) through: 7. PDF One-Step Word Problems I N 7MYa7d beB SwVi6tKh1 mInqf4i hn Si5t NeU APvrPeg-GAelegGedb2r Aa h.e Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ One-Step Equation Word Problems Date_____ Period____ 1) Lisa is cooking muffins. The recipe calls for 7 cups of sugar. She has already put in 2 cups. How many more cups does she need to put in? 2 ... 8. PDF Systems of Equations Word Problems Systems of Equations Word Problems. 2) Flying with the wind a plane went 183 km/h. Flying into the same wind the plane only went 141 km/h. Find the speed of the plane in still air and the speed of the wind. 3) Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. 9. PDF Infinite Pre-Algebra Worksheet by Kuta Software LLC Intermediate Algebra 2.4 Modeling With Linear Equations Worksheet Name_____ ID: 1 Date_____ ©I y2W0z1J6i vKIuKtpaW hSJoRfGthwKaarYeR pLWLzCF.R X EAQlVlJ qrDiKgChjtWsJ lrtetsTeGrzvAe`dF.-1-1) Dan bought eight CDs. A week later half of all his CDs were destroyed in a fire. 10. Infinite Algebra 1 Test and Worksheet Generator for Algebra 1 Infinite Algebra 1 covers all typical algebra material, over 90 topics in all, from adding and subtracting positives and negatives to solving rational equations. Suitable for any class with algebra content. Designed for all levels of learners from remedial to advanced. Beginning Algebra 11. Free Printable Math Worksheets for Pre-Algebra The Pythagorean Theorem. The distance formula. The midpoint formula. Classifying triangles and quadrilaterals. Angle sum of triangles and quadrilaterals. Area of triangles. Area of squares, rectangles, and parallelograms. Area of trapezoids. Area and circumference of circles. 12. Infinite Pre-Algebra Fixed: Systems of Equations Word Problems - Page width options do the opposite of what they say ... New: Kuta Works - Option to hide answers and results from students until after due date; New: Kuta Works ... Fixed: Writing Linear Equations - directions didn't always match the problem; Included in version 2.02 released 8/5/2014: 13. Infinite Algebra 2 Test and Worksheet Generator for Algebra 2. Infinite Algebra 2 covers all typical Algebra 2 material, beginning with a few major Algebra 1 concepts and going through trigonometry. There are over 125 topics in all, from multi-step equations to trigonometric identities. Suitable for any class with advanced algebra content. 14. PDF Systems Word Problems Kuta Software - Infinite Pre-Algebra Name_____ Systems of Equations Word Problems Date_____ Period____ 1) Kristin spent$131 on shirts. Fancy shirts cost $28 and plain shirts cost$15. If she bought a total of 7 then how many of each kind did she buy? 2) There are 13 animals in the barn.

15. PDF Infinite Algebra 1

Worksheet by Kuta Software LLC-2-Establish a variable. Write an equation. Solve your equation and label your answer. 7) Mia won 77 pieces of gum playing hoops at her school's game night. Later, she gave three to each of her friends. She only has 5 remaining. How many friends does she have? 8) Devin paid $30 to be a member of the Fox Lake Gym. 16. 1.20: Word Problems for Linear Equations 1: Chapters 1.20: Word Problems for Linear Equations 17. Linear Equation Word Problems Summary. When writing linear equations (also called linear models) from word problems, you need to know what the x and y variables refer to, as well as what the slope and y-intercept are. Here are some tricks to help translate:. The x variable. Usually, you'll be asked to find an equation in terms of some factor. This will usually be whatever affects the output of the equation. 18. Linear equations word problems Linear equations word problems. Google Classroom. Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. H represents the height of the tree (in centimeters), t years since Renata moved in. H = 210 + 33 t. 19. PDF 6.1--6.3--Solving Systems of Equations--Word Problems 1) One number is four less than eleven times another. The sum of the two numbers is 92. What are the numbers? 2) Cory has$24 more than twice as much as Stan. Together they have $150. How much money does each have? 3) Bill Legg is the place kicker for his high school football team. Last season he kicked 38 times and never missed. 20. PDF Linear Equations 1.8 Linear Equations - Word Problems Word problems can be tricky. Often it takes a bit of practice to convert the english sentence into a mathematical sentence. This is what we will focus on here with some basic number problems, geometry problems, and parts problems. 21. Word Problems Linear Equations Show Answer 10 weeks ($155) \ (\textbf {2)}\) Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did each of them collect? Show Equations \ (m+s=50,\,\,\,m=s+10\) Show Answer Mike collected 30 rocks, Sarah collected 20 rocks.

22. Inequalities Word Problem Worksheet

Worksheet by Kuta Software LLC-3-Answers to Inequalities Word Problem Worksheet 1) No more than 12 weeks2) No more than 12.7 miles3) No more than 5 DVDs 4) At least 12 more sessions5) At least 950 bags of dog food. 6) More than 12.5 weeks. 7) At least 15 times 8) No solution. : 1012141618 9) n > -5: -6-4-202 10) x £ -1: -4-20246 11) No solution.

23. Word Problems on Linear Equations

Step-by-step application of linear equations to solve practical word problems: 1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers. Let the number be x. Therefore, the two numbers are 8 and 17. 2.The difference between the two numbers is 48. The ratio of the two numbers is 7:3.