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## Unit 10: Lesson 1

- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example

## Linear equation word problems — Basic example

- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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## Video transcript

## 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.

More solved examples with detailed explanation on the word problems on linear equations.

How to Solve 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

Worksheet on Word Problems on Linear Equation

7th Grade Math Problems 8th Grade Math Practice From Word Problems on Linear Equations to HOME PAGE

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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

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

## Word Problems: Linear Models

Word problems sometimes ask us to write a linear function to model a situation.

In other problems, it may be easier to use the point-slope form of the equation.

First, find the rate of change. Be sure to multiply the distance by 2 : he has to go and come back!

2 ( 332 ) = 664 miles per week

Note that you can use this equation to find the y -intercept if you want to.

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## COMMENTS

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, ... Linear equations word problems. CCSS.Math: HSF.

Learn for free about math, art, computer programming, economics, physics, ... Watch Sal work through a basic Linear equations word problem.

Word Problems Linear Equations · \textbf{1)} Joe and Steve are saving money. · \textbf{2)} Mike and Sarah collect rocks. · \textbf{3)} In a classroom the ratio of

Word Problems on Linear Equations · Then the other number = x + 9. Let the number be x. · 2.The difference between the two numbers is 48. · 3. The length of a

Just like any other word problem, linear equation word problems are translated, then solved. Look for a rate of change and a y-intercept.

1.20: Word Problems for Linear Equations · 5% · 5%⋅$2.40. · 5%⋅2.40=0.05⋅2.40=0.1200=0.12 · 2.40+0.12=2.52 · $2.52 · $12 · x · 12⋅3⋅x=180.

Linear equation word problem | Linear equations | Algebra I | Khan Academy. Fundraiser.

Assume that the cost, y, is a linear function of the number of x people. Write an equation in slope-intercept form for this function. What does the slope

Solving Linear Equations In Word Problems : Example Question #1 ... Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling

The word problem may be phrased in such a way that we can easily find a linear function using the slope-intercept form of the equation for a line.