You buy a pair of tennis shoes on sale for $48. The price is discounted 25% and the sales tax is 7 %. would it cost less to have the discount applied before the sales tax is added or after the sales tax is added? Explain.
now remember what percentages mean ("over 100," i'm sure you've seen that around here before). so 7% = 7/100 = 0.07 and 25% = 25/100 = 0.25, 75% = 75/100 = 0.75
we begin with 48
if we apply sales tax first we get: 48 * 1.07 = 51.36
now take the 25% discount (you will pay 75% of the amount): 51.36 * 0.75 = 38.52
so we pay $38.52 if sales tax is applied first.
if we begin with 48 and we apply the discount first, we end up with:
(we pay 75% of the amount): 48 * 0.75 = 36.00
now apply the sales tax, we will pay: 36 * 1.07 = 38.52
so, no, one does not cost less than the other, they cost the same. this makes sense, since when applying the sales tax or the discount what we were doing was multiplying the original amount by some number. multiplication is commutative, so it doesn't matter which number we multiply by first, you will get the same answer in the end