A sweater originally costs $80. It is placed on sale for off the original price. After the discount is applied, a sales tax of is added to the discounted price. What is the final cost of the sweater, in dollars?
A discount followed by sales tax is a pair of successive percent changes: the second change applies to the price after the first. Find the percent of the price left after the discount, then the percent of that price owed after tax. Put those changes in order in one Desmos expression. Don’t combine the percentages as if both used the original price.
Hints
- Hint 1
A discount takes part of the original price away. Start with the full and subtract the discount percentage. What percent of the original price is left?
- Hint 2
The base of a percent is the amount it acts on. Because tax comes after the sale, its base is the discounted price, not the original price. What percent of that base do you owe after tax?
- Hint 3
In Desmos, put the discount calculation inside parentheses, then take the tax-adjusted percent of it. The calculation inside the parentheses happens first, matching the order in the question.
Step-by-step
Apply the discount, then the tax
Step 1Find the percent left after the discount
The discount takes away part of the original price, so start with the full . Subtract the discount to find the percent left:
- Step 2
Find the discounted price
Type in Desmos. It prints , so the sweater costs $60 before tax. Don’t stop here: the question asks for the cost after tax.
- Step 3
Find the percent owed after tax
The base, the amount a percent acts on, is now the discounted price, not the original $80. Add the tax to the full of that price: . Each percent acts on the price left by the change before it.
- Step 4
Calculate the final cost
Type on the next Desmos line. The discount happens inside the parentheses first. Desmos prints , so the final cost is $64.80. Choice C.