# WRITING TWO STEP EQUATIONS

We can write two-step equations to represent real-world problems by translating the words of the problems into numbers, variables, and operations.

Example 1 :

A one-year membership to Metro Gym costs \$460. There is a fee of \$40 when you join, and the rest is paid monthly. Write an equation to represent what you will pay monthly for the yearlong membership. Write an equation that would help members find how much they pay per month.

Solution :

Step 1 :

Identify what we are trying to find. This will be the variable in the equation.

Let m represent the amount of money members pay per month.

Step 2 :

Identify important information in the problem that can be used to help write an equation.

One-time joining fee : \$40

Fee charged for 1 year (= 12 months) : 12·m

total cost for the year : \$460

Step 3 :

Use words in the problem to tie the information together and write an equation. The equation 40 + 12m  =  460 can help members find out their monthly fee.

Example 2 :

Billy has a gift card with a \$150 balance. He buys several video games that cost \$35 each. After the purchases, his gift card balance is \$45. Write an equation to help find out how many video games Billy bought.

Solution :

Step 1 :

Identify what we are trying to find. This will be the variable in the equation.

Let n represent the number of video games that Billy bought.

Step 2 :

Identify important information in the problem that can be used to help write an equation.

Cost of one video game : \$35

Number of video games bought by Billy : n

Total purchase : 35·n

Step 3 :

Use words in the problem to tie the information together and write an equation.

Initial balance minus total purchase equals balance after purchase.

\$150 - 35n  =  \$45

The equation 150 - 35n  =  45 can help Billy to find out how many video games he bought

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