A reverse percent change gives you a sale price and asks for the price before the discount. First find what percent of the original price remains. Then set that percent of the unknown original equal to the sale price and solve with a Desmos regression. Adding a percent of the sale price back uses the wrong starting amount.
Hints
- Hint 1
A discount removes part of the starting price. The whole original price is . After a discount, what percent of that original price is left?
- Hint 2
The base is the amount a percent is taken of. Here the base is the unknown original price, not the sale price. If is the original price, what percent of equals $48?
Step-by-step
Work backward from the sale price
Step 1Find the percent left after the discount
A discount is the part removed from the original price. The jacket starts at of that price, so subtract the removed to find what's left:
- Step 2
Connect the sale price to the original
Let be the original price in dollars. The given $48 is the left after the discount, so:
The discount is a percent of the original price, not the sale price.
- Step 3
Solve for the original price
Type in Desmos. The stands for the unknown original price, and tells Desmos to solve for it. Under PARAMETERS, Desmos shows . So the jacket's original price was $64. Choice B.