Answer to Question #240206 in Calculus for inin

Question

A new pizzeria has opened near you home, the owner has decided to offer a 20% discount on

the opening day on the pizza whose original price is x dollars. The owner is offering additional

15% discount coupon to those who agree to fill a feedback form afterwards. You and your

friends have agreed to provide feedback and thus have become entitled to the additional 15%

discount coupon. Use the concept of composite functions to identify the amount that you will

pay after applying the coupon on the sale price.

Answer 1

Let x be the initial price of pizza. The discount is 20%, so the real price of pizza is $100\%-20\% =80\%$ from the initial price, or 0.80x.

Next, there are two possible options.

1) If the discount coupon is applied to the initial price and is combined with a discount of 20%, we get the total discount 35% and we pay only 0.65x.

2) If the discount coupon is applied to price after applying a 20% discount, we obtain the final price $0.8x - 0.15\cdot 0.8x = 0.85\cdot0.8x = 0.68x$, so the first discount is 20% from the initial price and the second discount is 15% of 0.8x or 12% from the initial price and the total discount is 32%.