# Word Problems Involving Two-Step Linear Equations

It's not always easy to tell what kind of equation a word problem involves, until you start translating it to math symbols.

Before solving equations , let's discuss about how we can write a two-step equation from a verbal model. The following table explains the keywords used when writing equations from verbal models.

 Addition Subtraction Multiplication Division sum difference product quotient plus less than times divided and subtract split up altogether left combined decreased more than increased

Example 1:

Six less than two times a number is equal to nine.

Identify any key words that identify operations.

Six less than two times a number is equal to nine.

The phrases "less than " indicates subtraction and "two times" indicates multiplication by $2$ , i.e., $2n$ .

So, the equation becomes $2n-6=9$ .

Example 2:

Brent paid $121$ for shoes and clothes. He paid $45$ more for clothes than he did for shoes. How much did Brent pay for he shoes?

Let $s$ be the amount paid for the shoes.

The amount paid for clothes is $45$ more than the amount paid for shoes.

The phrase "more than" indicates addition.

So, an expression for the amount paid for clothes is $s+45$ .

The total amount paid is the sum of the amount paid for shoes and that for clothes.

So, an equation that represents the situation is

$121=s+\left(s+45\right)$

Combine the like terms.

$121=2s+45$

Subtract $45$ from each side.

$76=2s$

Divide each side by $2$ .

$38=s$

So, Brent paid $38$ for the shoes.