Question 14·Medium·Percentages
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?
For percent discount or markup questions, quickly convert the situation into the equation "part = percent × whole." A discount of 20% means you pay 80% of the original price, so write something like and solve by dividing. Always check your result by mentally applying the percent to see if it reproduces the given amount.
Hints
Think about what percent you actually pay
If the store takes 20% off the original price, what percent of the original price do you still have to pay?
Write an equation with a variable
Let be the original price. The sale price, $64, is some percent of . What decimal can you multiply by to represent the price after a 20% discount?
Solve the one-step equation
Once you have an equation like , isolate by doing the same operation to both sides of the equation.
Desmos Guide
Use Desmos to compute the original price
In the Desmos calculator, type 64/0.8 (or 64/(1-0.2)) and press Enter. The value that appears is the original price before the 20% discount; match that number to the closest answer choice.
Step-by-step Explanation
Translate the discount into a percent you pay
A 20% discount means you do not pay 20% of the original price.
Instead, you pay the remaining percent:
- 100% (the full price) (discount) (you actually pay)
So the sale price ($64) is 80% of the original price.
Set up an equation
Let be the original price of the jacket, in dollars.
Since you pay 80% of the original price and that equals $64, write:
Here, is 80% written as a decimal.
Solve for the original price and match the choice
Solve the equation by dividing both sides by :
Compute this:
So the jacket’s original price was $80, which corresponds to choice D) 80.