During a sale, a store lowered the price of a jacket by 25%, resulting in a sale price of $45. What was the original price of the jacket, in dollars, before the discount?
A sale price given after a discount, with the starting price missing, is a reverse percent change. Find what percent of the original price is still paid, then write that percent of the unknown original equal to the sale price. Use a Desmos regression to solve. The tempting slip is to add the discount percent to the sale price, even though the discount was taken from the original.
Hints
- Hint 1
A discount removes part of the starting price. Start with the whole and take away the discount. What percent of the original price does the customer pay?
- Hint 2
The base is the amount a percent is taken of. Here, that’s the unknown original price, not the sale price. Call it and put it after “of” when you write the sale-price equation.
Step-by-step
Work backward from the sale price
Step 1Find the percent still paid
The base for the discount is the original price, which counts as . Subtract the taken off to find the share still paid:
- Step 2
Connect the sale price to the original
Let be the original price in dollars. The sale price is $45, so of the original equals :
The unknown original belongs after “of.” Taking a percent of $45 instead would use the sale price as the base.
- Step 3
Solve for the price before the discount
Type in Desmos. A regression finds a value that makes the two sides equal: tells Desmos to solve for a number instead of graphing , and replaces . Under PARAMETERS, Desmos shows . So the original jacket price was $60. Grid in 60.