Question

2 mai and elena are shopping for back-to-school clothes. they found a skirt that originally cost $30 on a 15%-off sale rack. today, the store is offering an additional 15% off. to find the new price of the skirt, in dollars, mai says they need to calculate 30·0.85·0.85. elena says they can just multiply 30·0.70. a. how much will the skirt cost using mai’s method? b. how much will the skirt cost using elena’s method? c. explain why the expressions used by mai and elena give different prices for the skirt. which method is correct?

Explanation:

Step1: Calculate first discount (Mai)

$30 \times 0.85 = 25.5$

Step2: Apply second discount (Mai)

$25.5 \times 0.85 = 21.675$

Step3: Calculate Elena's method

$30 \times 0.70 = 21$

Step4: Explain discount difference

Successive discounts apply to reduced price, not original.

Answer:

a. $\$21.68$ (rounded to nearest cent, or $\$21.675$)
b. $\$21$
c. Mai's method is correct. Elena incorrectly assumes two 15% discounts equal a total 30% discount, but each 15% discount is applied to the already discounted price, not the original $\$30$. The first 15% off reduces the price to 85% of the original, and the second 15% off reduces that new price to 85% of itself, which is not the same as 70% of the original price.