Solve Applications with Systems of Equations

Question

A coffee shop offers a special "Coffee Club" program where you pay a membership fee of $11 each month but then you get a 17% discount on all coffee purchases. How much would you need to spend on coffee each month for the membership to save you money?

Answer 1

Cost = 11 + 0.83C where C = number of coffee purchases times the price of each coffee. 17% off means you pay 83% of regular price

K=11+0.83C

C-0.83C = 11

.17C = 11

C = 11/.17 = about 64.71 = price of coffee times number of coffee purchases plus the 11 fee. You'd need to spend at least $54.71 per month on coffee at the 17% discounted rate for the $11 fee and discount to be worthwhile.

54.71 at discounted rate means 54.71/.83 = regular cost = about 65.9 > 64.71

You save money as soon as you spend $54.71 or more on coffee purchases per month, if you have the discounted rate.