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=zB. x=y

Answer 1

B. x=y

Explanation:

A 5% tax charge is equivalent to multiply the current price by 1.05. On the other hand, a 5% discount is equivalent to substrace the current the 5% of it, so in the end, you multiply the current price by 0.95.

For X we should multiply first by 0.95, then by 1.05

For Y we multiply first by 1.05, then by 0.95

Hence, if L = price list, we have

• x = L*0.95*1.05 = 0.9975L
• y = L*1.05*0.95 = 0.9975L
• z = L

As a result, x=y<z. Option B is correct.

Note that applying discount first or charging taxes first doesnt matter because the order of the factors doesnt ater the product.