Amy paid $66.66 for a pair of running shoes during a 35%-off sale. What was the regular price?

Let the original price be P

(1.00 - 0.35) P = 66.66
0.65 P = 66.66
P = 66.66/0.65 = 102.55

To find the regular price of the running shoes, we first need to determine the amount of the discount applied.

The amount of discount can be found by multiplying the regular price by the discount rate (35%).
Discount = Regular Price x Discount Rate

Let's represent the regular price with the variable 'x'. The discount can be calculated as follows:
Discount = x * 35/100

Now, we can calculate the discounted price by subtracting the discount from the regular price:
Discounted Price = Regular Price - Discount

In this case, we know that the discounted price is $66.66. So we have the following equation:
$66.66 = x - (x * 35/100)

To solve for x, we can simplify the equation:
$66.66 = x * (1 - 35/100)
$66.66 = x * (1 - 0.35)
$66.66 = x * 0.65

Now, isolate x by dividing both sides of the equation by 0.65:
x = $66.66 / 0.65

Using a calculator, we can find the value of x:
x ≈ $102.56

Therefore, the regular price of the running shoes was approximately $102.56.