Question 2·Medium·Percentages
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?
For percent discount plus tax problems, treat each percent as a multiplier on the price and apply them in order. A discount of means multiply by , and a tax of means multiply by . Multiply the original price by both factors (for this problem, ) to get the final price in one or two quick calculator steps, and be careful to base the tax on the already-discounted price, not the original price.
Hints
Separate the discount and the tax
Handle the price reduction and the sales tax as two separate steps: first apply the 25% discount to $80, then deal with the 8% tax.
Find the discounted price first
What is 25% of 80? Subtract that amount from 80 to find the sale price before tax.
Use the discounted price as the base for tax
The 8% sales tax is charged on the discounted price, not the original $80. Multiply the discounted price by 0.08 to get the tax amount.
Combine for the final price
Once you know the discounted price and the tax amount, add them together to get the final cost of the sweater.
Desmos Guide
Calculate the discounted-and-taxed price in one expression
In a Desmos expression line, type 80*0.75*1.08 (since 25% off is multiplying by 0.75 and adding 8% tax is multiplying by 1.08). The numerical output shown by Desmos is the final cost of the sweater.
Step-by-step Explanation
Find the sale (discounted) price
The sweater is 25% off the original $80.
- Find 25% of 80:
- Subtract this discount from the original price:
So, the discounted price of the sweater is $60 (before tax).
Calculate the 8% sales tax on the discounted price
Sales tax is 8% of the discounted price, which is $60.
Compute 8% of 60:
So the tax amount is $4.80. (We will add this to the $60 sale price.)
Add the tax to the discounted price to get the final cost
Now add the tax to the discounted price:
So, the final cost of the sweater is $64.80, which corresponds to answer choice C) 64.80.