If a bookstore has a promotion, where you get 10% off all products or you can buy a $36 membership and get 25% off all products, how much would you have to spend to save money?
Getting 10% off means you are spending 90% of the full price.
Getting 25% off means you are spending 75% of the full price.
Paying $36 plus 0.75 * $x has to equal paying 0.9 * $x to find the breakeven point.
$x is the full price of the books.
$36 + (0.75 * $x) = 0.9 * $x
$36 = (0.9 * $x) - (0.75 * $x) = 0.15 * $x
$36 / 0.15 = $x = $240
If you buy $240 worth of merchandise and get a 10% discount,
you will pay $216.
If you buy $240 worth of merchandice and get a 25% discount,
you will pay $180, but to get that discount, you must pay $36
upfront, bringing the total to $216.
After $216, any purchase through the membership saves you money.