Question

Tim purchased a pair of running shoes for $79.20, which included 10% sales tax. If the shoes were on sale for 40% off the original price, what was the original price of the running shoes?

Answer 1

To find the original price of the running shoes, divide the final price by 1 minus the discount rate, and then divide the price before the discount by 1 plus the tax rate.

Step-by-step explanation:

To find the original price of the running shoes, we need to reverse the effects of the 40% off discount and the 10% sales tax. Let's break it down:

1. Step 1: Convert the final price of $79.20 to the price before the discount was applied.
2. Step 2: Convert the price before the discount to the original price.

Step 1: To find the price before the discount, we can divide the final price by 1 minus the discount rate:

$79.20 / (1 - 0.40) = $79.20 / 0.60 = $132

Step 2: To find the original price, we need to remove the effect of the sales tax. Since the sales tax is 10%, we can divide the price before the discount by 1 plus the tax rate:

$132 / (1 + 0.10) = $132 / 1.10 = $120

Therefore, the original price of the running shoes was $120.