Question

Two stores have the same item for the same price. • Store A offers successive discounts of 5% one week, 10% the next week, and 10% the third week. • Store B offers one discount of 25% the third week. Which offer results in the greater discount? Justify your answer. Show your work.

Answer 1

Step-by-step explanation: To compare the discounts offered by Store A and Store B, we need to calculate the final price of the item after all discounts have been applied.

For Store A, the successive discounts of 5%, 10%, and 10% can be applied as follows:

The initial price of the item is reduced by 5%, resulting in a price of 0.95 * Price.

The price from step 1 is reduced by an additional 10%, resulting in a price of 0.9 * (0.95 * Price) = 0.855 * Price.

The price from step 2 is reduced by an additional 10%, resulting in a price of 0.9 * (0.855 * Price) = 0.7695 * Price.

For Store B, the single discount of 25% can be applied as follows:

The initial price of the item is reduced by 25%, resulting in a price of 0.75 * Price.

Comparing the final prices of the item at Store A and Store B, we can see that Store B offers a greater discount. The final price of the item at Store A is 0.7695 * Price, while the final price at Store B is 0.75 * Price. Since 0.75 is less than 0.7695, the final price at Store B is lower.

Therefore, Store B offers a greater discount on the item.

Answer 2

Below

Explanation:

10 % OFF means you pay 90% of price

x = original price

Store A : 5% off means price is .95x

then another 10% off would mean .9 * (.95x)

then another 10% off would mean .9 * ( .9 *(.95x)

this equals .7695 x

Store B 25% off means you pay 75%

price is then .75x

price of .75x at store B is < than .7695 x at store A

so B has greater discount