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 discounts first and then charges sales 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

Question

Mathematics

Austin

17 November, 20:02

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 discounts first and then charges sales 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

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Sunny · Answer 1

x=y
Step-by-step explanation:

Lets calculate how much money the stores charge with respect to the price list.

Since Z does not charge with taxes or discounts, then Z sells 100 % the price list.

X applies a discount first, so it sells at 95% the price ignoring taxes. With the tax charge it increases by a 5% of the 95, so in total it sells with 95 + 95 * (0.05) = 99.75 %

Y charges with taxes first, so it the prices increases by a 5% to a total of 105% the list price, and then makes a discount, so the total price is 105-105*0.05 = 99.75%

As a result

x = 99.75%

y = 99.75%

z = 100%

Therefore x=y