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?
If you buy $1,000,000 worth of products, then of course the membership is a better deal. The question is where the non-membership deal and the membership deal are equal.
x = sticker price of what you buy
x * 0.90 (10% off)
x * 0.75 + 36 (25% off with $36 membership)
0.9x = 0.75x + 36
0.15x = 36
x = 240
If you buy less than $240 worth of products, the non-membership is a better deal.
If you buy $240 worth of products, the non-membership deal is the same as the membership deal.
If you buy more than $240 worth of products, the membership is a better deal.