Amy paid $77.71 for shoes during a 20% off sale. What is the regular price of the shoes?

100% - 20% = 80% = 0.80,

0.8p = 77.71,
P = 77.71/0.8 = 97.14

To find the regular price of the shoes, you need to reverse the discount amount and calculate it as a percentage of the sale price. Here's how you can do it:

1. Determine the discount amount:
- The shoes were purchased with a 20% off sale.
- 20% of the regular price is equivalent to paying 80% of the regular price.

2. Calculate the sale price:
- If Amy paid $77.71, this amount represents 80% of the regular price.
- So, to calculate the sale price, you can simply divide $77.71 by 0.80.

Let's calculate it:

Sale price = $77.71 ÷ 0.80
Sale price ≈ $97.14

Therefore, the regular price of the shoes is approximately $97.14.