Question 52·Easy·Percentages
A jacket is advertised at a 25% discount off its original price. The sale price is $48. What was the jacket’s original price?
For percent discount problems, first convert the discount to the percent you actually pay (100% minus the discount). Translate that relationship into an equation like (percent paid as a decimal) × original = sale price, then solve by dividing the sale price by the decimal. On multiple-choice questions, you can quickly check your result by taking the given discount off your computed original price to see if you get the listed sale price.
Hints
Think about what percent you still pay
If a store takes 25% off the original price, what percent of the original price do you actually pay at the register?
Write an equation
Let be the original price. If the sale price is 75% of the original, how can you write that as an equation involving and 48?
Isolate the original price
Your equation should look like . What operation will undo multiplying by ?
Check with the discount
After you find , take 25% of that number and subtract it. Do you get a sale price of $48?
Desmos Guide
Use Desmos to compute the original price
In the expression line, type 48/0.75 and press Enter. The numerical result shown by Desmos is the value of that solves , which represents the jacket’s original price.
Step-by-step Explanation
Translate the percent discount into the percent you pay
A 25% discount means you are not paying 25% of the original price.
So you are paying the remaining percentage:
- of the original price.
That means the sale price ($48) is 75% of the original price.
Set up an equation for the original price
Let be the original price of the jacket.
If the sale price is 75% of the original price, then:
This equation says: 75% of equals the sale price, $48.
Solve the equation for the original price
To solve , divide both sides by :
This gives the original price in dollars.
Compute and match with the answer choices
Now compute , which equals 64.
So the jacket’s original price was $64, which matches choice B.