Question

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?

Answer 1

See a solution process below:

Explanation:

A formula to solve this problem is:

`e = p * h * 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`

`(3272.50color(red)(" wks"))/color(blue)(297.50) = w`

`11 " wks" = w`

John has worked at Buy-The-Best for `color(red)(11)` weeks.