A jacket is on sale for $64 after a 20% discount is applied to the original price. What was the jacket’s original price, in dollars?
A reverse percent change question gives you a price after a discount and asks for the price before it. Find the percent that remains, then use a Desmos regression to solve for the original price. The discount is taken from the original price, not the sale price. Adding a percent of the sale price back uses the wrong amount.
Hints
- Hint 1
A discount is the part taken away from the original price. Start with the whole price, or , and subtract the discount. What percent of the original is still paid?
- Hint 2
The base is the amount a percent is taken of. Here, the base is the price before the discount, not the sale price. Let an unknown stand for that original price.
Step-by-step
Solve from the percent left
Step 1Find the percent still paid
A discount takes away a percent of the original price. Subtract the discount from the whole price:
- Step 2
Connect the sale price to the original
Let be the original price. The sale price is of , so write: . Don't take of : the discount was taken from , not from the sale price.
- Step 3
Solve for the original price
Type in Desmos. The and tell Desmos to solve for the unknown rather than graph the equation. Under PARAMETERS, it shows . So the jacket’s original price was $80. Choice D.