Question

Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discount first and then charges tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z ?A. x=y=z
B. x=y C. x D. x E. y

Answer 1

Answer: B. x=y

Step-by-step explanation:

Store X applies its discount of 5% first and then charges tax of 5% on the discounted price. The discount is 5/100× x = 0.05x. The new amount is x - 0.05x = 0.95x

Tax charged on 0.95x = 5/100× 0.95x = 0.0475

Final amount at store x = 0.95x + 0.0475x = 0.9975x

Store Y adds the tax first and then applies the discount to the price with tax.

Tax charged on y = 5/100× y = 0.05y.

Price with tax = y + 0.05y = 1.05y

5% discount on 1.05y = 5/100 × 1.05y = 0.0525y

Final amount at store y = 1.05y - 0.0525y = 0.9975y

The final price at store Z remains z

The final prices at store X and store Y are 0.9975 of the initial prices. Therefore, X = Y describes the relationship among x, y, and z