Question

You want to buy a new pair of shoes. The coupon offers $25 off, and there's a 30% discount at the store. The discounted price is the same with either option. What was the original price of the shoes? How much did the shoes cost after the discount?

a) $100, $70
b) $80, $55
c) $120, $84
d) $150, $105

Answer 1

The original price is approximately $83.33, but none of the answer choices exactly match this. Considering the closest whole dollar amount, option (b) with an original price of $80 is the closest, making the post-discount shoes cost $55.

Step-by-step explanation:

The question is a math problem involving proportions and percentages.

To find the original price of the shoes, let's assume the original price is X dollars. With the $25 off coupon, the cost of the shoes would be (X - $25). With the 30% discount, the cost would be (0.7 * X).

Since the discounted price is the same with either option:
(X - $25) = 0.7 * X

1. Multiply both sides by 10 to clear decimals: 10(X - 25) = 7X
2. Distribute on left: 10X - 250 = 7X
3. Subtract 7X from both sides: 3X = 250
4. Divide by 3: X = $83.33 (approximately)

Since none of the answer choices exactly match $83.33, and we're looking for the closest whole dollar amount, out of the given options, option (b) with an original price of $80 is the closest.

The shoes cost $55 after a $25 discount, which is similar to a 30% discount off the original price of $80 (which would be $56).