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?

Question

Eva Adamson · Accepted Answer

undefined To find the number of weeks John has worked at Buy-the-Best, divide his total earnings ($3,272.50) by his hourly rate ($8.50). This gives us the total number of hours worked. Then, divide this total number of hours by the number of hours he works per week (35 hours). This will give us the number of weeks he has worked.

$3,272.50 / $8.50 per hour = 385 hours
385 hours / 35 hours per week = 11 weeks

John has worked 11 weeks at Buy-the-Best.

Nathan Axel · Answer

See a solution process below:

Here is a formula to solve this issue: #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. When the values from the problem are substituted, we get: #$3272.50 = ($8.50)/"hr" * (35 "hrs")/"wk" * w# The common terms in the denominators and numerators can first be eliminated: #$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.