Question

Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression that can be used to determine the final cost of the DVD

Answer 1

0.88%y + 0.03%

The previous answer showed no expression.

Answer 2

"on sale for 12% off" means that whatever the price is (y) we multiply it by 0.88 since 1-0.12 = 0.88

Price before discount = original price = y

Price after discount = 0.88y

Put another way, we took 88% of the original price to get the discount price.

------------------------------------

Now tack on the sales tax. We do this by multiplying the discount price by 1.03 (1 + 0.03 = 1.03)

So we have:

final cost = 1.03*(discount price)

final cost = 1.03*(0.88y)

final cost = 0.9064y

telling us that the final cost is 90.64% of the original price (y). With the tax added, the discount is not 12% but actually 100% - 90.64% = 9.36%