# John worked 35 hours a week at Buy-the-Best for $8.50 per hour. So far, he has earned$3,272.50. How many weeks has John worked at Buy-the-Best?

Aug 8, 2017

See a solution process below:

#### Explanation:

A formula to solve this problem is:

$e = p \cdot h \cdot w$

Where:

$e$ is the total earnings. $3,272.50 for this problem. $p$is the hourly pay.$8.50/hr for this problem.

$h$ is the number of hours worked. 35 hrs/wk for this problem.

$w$ is the number of weeks worked. What we are solving for in this problem.

Substituting the values from the problem gives:

$3272.50 = ($8.50)/"hr" * (35 "hrs")/"wk" * w

First, we can cancel the common terms in the numerators and denominators:

$3272.50 = ($8.50)/color(red)(cancel(color(black)("hr"))) * (35 color(red)(cancel(color(black)("hrs"))))/"wk" * w

$3272.50 =$8.50 * 35/"wk" * w

$3272.50 = ($297.50)/"wk" * w

We can now multiply each side of the equation by color(red)("wk")/color(blue)($297.50) to solve for $w$while keeping the equation balanced: color(red)("wk")/color(blue)($297.50) xx $3272.50 = color(red)("wk")/color(blue)($297.50) xx ($297.50)/"wk" * w color(red)("wk")/color(blue)(color(black)(cancel(color(blue)($)))297.50) xx color(blue)(cancel(color(black)($)))3272.50 = cancel(color(red)("wk"))/cancel(color(blue)($297.50)) xx color(blue)(cancel(color(black)($297.50)))/color(red)(cancel(color(black)("wk"))) * w $\frac{3272.50 \textcolor{red}{\text{ wks}}}{\textcolor{b l u e}{297.50}} = w$$11 \text{ wks} = w$John has worked at Buy-The-Best for $\textcolor{red}{11}\$ weeks.