A reverse percent change gives the price after a discount but asks for the original price. Find the percent left, then set that percent of the unknown original equal to the sale price and solve with a Desmos regression. The discount is based on the original, not the sale price. Adding a percent of the sale price back uses the wrong base.
Hints
- Hint 1
Before a discount, the price is 100% of itself. A discount takes away a percent of that original price. What percent remains after 15% is removed?
- Hint 2
The base of a percent is the amount it's taken of. Here the base is the unknown original price, not . If you call that price , what percent of equals ?
Step-by-step
Work backward from the sale price
Step 1Find the percent left
The full price is . A discount removes part of that price, so subtract to find the percent left:
- Step 2
Write the sale-price equation
Let be the original price, the amount the discount is taken of. The jacket costs $68 after the discount, so of equals :
- Step 3
Solve for the original price
Type in Desmos. Use instead of and instead of so the regression finds the value that makes the equation true. Under PARAMETERS, Desmos shows . So the jacket's original price was $80. Choice C.