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## Linear Equation Word Problems Worksheet

Students will practice solving linear equation word problems.

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## Equation Word Problems Worksheets

One Step Equation Word Problem Worksheets

Two-Step Equation Word Problems: Integers

Two-Step Equation Word Problems: Fractions and Decimals

MCQ - Two-Step Equation Word Problems

Multi-Step Equation Word Problems: Integers

Multi-step equation Word Problems: Fractions and Decimals

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## 1.20: Word Problems for Linear Equations

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:

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:\

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:

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

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

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:

\[x=\frac{60}{5}=12\nonumber\]

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:

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.

We solve this as follows. First, add \(x\) :

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

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

Solution: We have the equation:

Dividing both sides by 4 gives the answer: \(x=3\).

We solve for \(x\) by adding 7 on both sides of the equation:

After dividing by \(2,\) we obtain the answer \(x=8\)

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.

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

\[12 \cdot 3 \cdot x=180\nonumber\]

\[x=\frac{180}{36}=5\nonumber\]

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

Combining the like terms on the left, we get

\[x=\frac{300}{5}=60\nonumber\]

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

Distributing and collecting like terms give

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

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?

Multiplying both sides by 10 gives

Subtracting 64 from both sides gives

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

## Graphing linear equations word problems worksheet ( with answer key + pdf)

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## Conclusion

If you have any questions or comments, please let us know.

## Clues when a word problem requires linear equations:

- There are two different quantities involved: for instance, the number of adults and the number of children, the number of large boxes and the number of small boxes, etc.
- There is a value associated with each quantity: for instance, the price of an adult ticket or a children’s ticket, or the number of items in a large box as opposed to a small box.

## Steps involved in solving a linear equation word problem:

- Read the problem carefully and note what is given and what is required.
- Denote the unknown by the variables as x, y or any other alphabet.
- Extract the data from the mathematical statement by translating the problem to the language of mathematics
- 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
- A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

## Linear Equation Graph

There are two ways you can graph linear equations:

Method 1: Using two points to graph a linear equation

Method 2: Use the slope and y-intercept

Let’s look at the y-intercept first.

Start with the y-intercept and go 3 unit right

Connect the points, and you have the graph of your linear function

Step1 : Understand the problem:

The admission cost for 12 children and 3 adults was $162.

The admission cost for 8 children and 3 adults was $122.

Step 2: Translate the problem to an equation.

Let x represent the admission cost for each child.

Let y represent the admission cost for each adult.

The admission cost for 12 children plus 3 adults is equal to $162 .

The admission cost for 8 children plus 3 adults is equal to $122.

Step 3: Carry out the plan and solve the problem.

Subtract the second equation from the first.

Therefore, the cost of admission for each child is $10 and each adult is $14 .

Graphing linear equations word problems worksheet (answers+ pdf)

- The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.
- Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find their present ages.
- The two numbers are 8 and 17.
- Present age of Ron = 6 years and present age of Aaron = 1 year.

## Problem Solving:

Which venue charges less per student? How many students must attend for the total

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Linear Equation Word Problems Worksheet (pdf) and Answer Key. 31 scaffolded questions on simplifying imaginary numbers Home Worksheets Linear Equations Word Problems Linear Equation Word Problems Worksheet Mathworksheetsgo.com is now a part of Mathwarehouse.com. All of your worksheets are now here on Mathwarehouse.com. Please update your bookmarks!

In this chapter, we focus on word problems modeled by a linear equation and solve. Below is a table of common English words converted into a mathematical expression. You can use this table to assist in translating expressions and equations. ... Round your answer to the nearest cent. 2) Sari bought a $125 pair of shoes on sale for $93.75. What ...

Water flows into the tank at a rate of 8 gallons per minute. Write a linear equation to model this situation. Find the volume of water in the tank 25 minutes after Baxter begins filling the tank. 10. A video rental store charges a $20 membership fee and $2.50 for each video rented. Write and graph a linear equation (y=mx+b) to model this situation.

Linear Equations and Inequalities Finding slope from a graph Finding slope from two points Finding slope from an equation Graphing lines using slope-intercept form Graphing lines using standard form Writing linear equations Graphing linear inequalities Graphing absolute value equations Direct variation Systems of Equations and Inequalities

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SECTION 3.1: LINEAR EQUATIONS A. VERIFYING SOLUTIONS A linear equation is made up of two expressions that are equal to each other. A linear equation may have one or two variables in it, where each variable is raised to the power of 1. No variable in a linear equation can have a power greater than 1. Linear equation: 2𝑦𝑦= 3𝑥𝑥+ 1

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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.

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Step 1: Identify the variables Let x =the number of days. Let y =money. Step 2: Relate the values with given data The y-intercept is 68. The x-intercept is 14. The slope is -3. Step 3: Write the linear function Applying: Write a linear function to represent the following word problems.

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This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school.

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We solve this as follows. First, add x : 9 = 2 x + x so that 9 = 3 x Then the answer is x = 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: 5 x = x + 12. Subtracting x gives 4 x = 12. Dividing both sides by 4 gives the answer: x = 3.

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