"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.
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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%