Question 26·Medium·Percentages
A store marks a jacket down by . After the discount is applied, a sales tax of is added to the discounted price. Including both the discount and the tax, what percent of the jacket’s original price does a customer pay?
For chained percent changes (like a discount followed by tax), avoid adding or subtracting the percentages directly. Instead, convert each percentage to a multiplier on the original price: for a discount of , use ; for an increase or tax of , use . Multiply these factors together to get a single overall multiplier, then convert that multiplier to a percent to select the answer. Using an easy starting price like $100 can also make the arithmetic and interpretation faster.
Hints
Start by choosing a simple original price
It can help to pretend the jacket originally costs dollars, or even dollars, so you can see how each percent change affects the price.
Turn the 15% discount into a multiplier
After a 15% discount, do you pay 15% or 85% of the original price? Write the discounted price as a decimal times the original price.
Remember what a tax does
Sales tax is added to the discounted price. Should you multiply the discounted price by a number less than 1 or greater than 1 to represent a 6% tax?
Combine the effects
Once you have a multiplier for the discount and a multiplier for the tax, multiply them together. That product tells you what fraction of the original price the customer pays; then convert that to a percent.
Desmos Guide
Use Desmos to combine the percent changes
In a new expression line, type (1 - 0.15)*(1 + 0.06) and look at the decimal value Desmos gives. That decimal is the fraction of the original price the customer pays; move the decimal point two places to the right to convert it to a percent and match it to the closest answer choice.
Step-by-step Explanation
Represent the original price
Let the jacket’s original price be dollars.
We want to find what fraction of the customer pays after both the discount and the tax.
Apply the 15% discount
A 15% discount means the customer pays of the original price.
In decimal form, , so the discounted price is:
Apply the 6% sales tax to the discounted price
The 6% tax is added to the discounted price, and it is 6% of the discounted price, not of the original.
A 6% increase means you multiply by :
So the customer pays times the original price .
Multiply the factors and convert to a percent
Now multiply the two decimals:
So the final price is:
This means the customer pays of the original price, which is of the original price.
Therefore, the correct answer is 90.1% (Choice C).