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
$121=s+(s+45)$
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.