Question 34·Easy·Percentages
After a 15% discount, the price of a jacket is $68. What was the original price of the jacket before the discount?
For percent discount problems, always relate the sale price to the original price using (100% − discount%) of the original. Write an equation like (decimal form of remaining percent) × (original price) = (sale price), then solve by dividing to isolate the original price. Use quick estimation to check reasonableness: the original should be larger than the sale price, and the difference should match the given percent roughly (here, 15% of the original should be around the amount saved).
Hints
Relate discount to what you actually pay
If an item has a 15% discount, what percent of the original price do you actually pay at the register?
Write an equation
Let be the original price. Express the sale price, $68, as a percentage of using your answer from the previous hint.
Solve the equation
Your equation should look like a decimal times equals 68. How do you isolate when it is being multiplied by a decimal?
Desmos Guide
Enter the reversal of the discount
In Desmos, type 68/0.85 to represent dividing the sale price by 0.85 (since 68 is 85% of the original). The output shown by Desmos is the original price; compare that value to the answer choices.
Step-by-step Explanation
Translate the discount into a percentage of the original price
A 15% discount means you pay the remaining 100% − 15% of the original price.
So you pay:
That means the $68 sale price is 85% of the original price.
Set up an equation for the original price
Let be the original price.
Since 85% of the original price equals $68, write:
To solve for , divide both sides by :
Compute and match to the answer choices
Now compute :
- You can do this with a calculator, or
- Notice that , so
So the original price of the jacket was $80, which corresponds to choice C.