# 7.11: Two-Step Equations from Verbal Models

**At Grade**Created by: CK-12

**Practice**Two-Step Equations from Verbal Models

Kara works as a babysitter for the neighborhood she lives in. She is saving money to plant an amazing sustainable home garden. For each babysitting job she took on, Kara charged $4 for bus fare plus an additional $8 for each hour she worked. On Saturday, Kara earned $26 for the entire babysitting job.

Write an equation to represent this situation, where

In this concept, you will learn to write two-step equations from verbal models.

### Writing Two-Step Equations from Verbal Models

You solve equations like

But how can you solve the following equations?

In these equations you need to do two operations to each side of the equation to isolate the variable. However, before you do this, look at some examples of word problems that involve two steps.

Here is an example.

Change the following word problem into an equation.

Six times a number, plus five is forty-one.

First, change the language into number and symbols. “Times” means multiplication, “a number” since it is not identified is your variable

The answer is

Here is another example.

Change the following word problem into an equation.

Four less than two times a number is equal to eight.

First, change the language into an equation. “Less than” means subtraction but be careful about the order. “Times” means multiplication, “a number” is your variable

The answer is

### Examples

#### Example 1

Earlier, you were given a problem about Kara’s sustainable garden.

She is saving money to build one at home. She has a babysitting job where she earns $8 and hour, but she also charges $4 for bus fare. If she earned $26 in total, can you write and equation to represent this.

First, let

Next, re-phrase the text to make it easier to understand. Her total earnings were $4 plus the number of hours she worked times 8. This equals $26 the total amount earned.

Then, turn the language into numbers and symbols and write the equation. “Plus” means addition, “the number of hours” is the variable

The answer is

#### Example 2

Write an equation for this statement.

A number divided by two, and then added to six is equal to fourteen.

First, change the language into numbers and mathematical symbols. “A number” is your variable

Then, write the equation.

The answer is

**Write an equation for each word problem.**

#### Example 3

The product of five and a number, plus three is twenty-three.

First, translate the language into numbers and symbols. “The product of” means multiply what is in the parenthetical expression “five and a number,” “a number” is your variable

Then, write your equation.

The answer is

#### Example 4

Six times a number, minus four is thirty-two.

First, translate the language into numbers and symbols. “Times” means multiplication, “a number” is the variable

The answer is

#### Example 5

A number

First, translate the language into numbers and symbols. “A number

The answer is

### Review

Write each statement as two-step equations.

- Two times a number, plus seven is nineteen.
- Three times a number, and five is twenty.
- Six times a number, and ten is forty-six.
- Seven less than two times a number is twenty-one.
- Eight less than three times a number is sixteen.
- A number divided by two, plus seven is ten.
- A number divided by three, and six is eleven.
- Two less than a number divided by four is ten.
- Four times a number, and eight is twenty.
- Five times a number, take away three is twelve.
- Two times a number, and seven is twenty-nine.
- Four times a number, and two is twenty-six.
- Negative three times a number, take a way four is equal to negative ten.
- Negative two times a number, and eight is equal to negative twelve.
- Negative five times a number, minus eight is equal to seventeen.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 7.11.

### Resources

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In this concept, you will learn to write two-step equations from verbal models.

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