A sale price after a discount signals a reverse percent problem: you know the reduced price but need the original. Find the percent that remains, write it as a percent of the unknown original, and use a Desmos regression to solve the equation. Adding the discount percent to the sale price uses the wrong base because the discount was taken from the original price.
Hints
- Hint 1
A discount removes part of the original price. The full original price is , so what percent remains after is removed? That remaining percent describes the sale price.
- Hint 2
The original price is the unknown. Let it be , then write the sale price as the remaining percent of . Set that amount equal to the given sale price.
Step-by-step
Work backward from the sale price
Step 1Find the percent of the price that remains
The base is the amount a percent is taken of. The discount is taken from the original price, so the sweater sells for what remains after that discount:
- Step 2
Write the sale-price equation
Let be the original price in dollars. The sale price is of that price, and the problem says it is $34, so
The original price goes after “of.” Taking of $34 instead would discount the sale price again.
- Step 3
Solve for the original price in Desmos
Type . Change to and to so Desmos solves for the unknown rather than graphing . Under PARAMETERS, it shows . The sweater's original price was $40. Grid in 40.