Question

You have a coupon good for $5 off the price, p, of any large pizza. You also get a 15% discount on any pizza if you show your student ID. How much more would you pay for a large pizza if the cashier applies the coupon first, rather than the 15% discount first? Please show steps to this composite function.

Answer 1

3; all real numbers except x=2

0.75

Answer 2

If the coupon is applied first.
Amount paid = $0.85(p - 5)

If the discount is applied first.
Amount paid = $0.85p - 5

Amount paid more if the coupon is applied first is 0.85(p - 5) - (0.85p - 5) = 0.85p - 4.25 - 0.85p + 5 = 0.75

Therefore, you will pay $0.75 more if the coupon is applied first rather than the 15% discount first.