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Difficulty: MediumCalculating Percentages of Quantities

An electronics store on a military base sells a laptop originally priced at 840840. The store offers a 25%25\% discount for service members. If a 6%6\% sales tax is applied to the discounted price, what is the final cost of the laptop?

  1. A
    680.40680.40
  2. B
    1008.001008.00
  3. 667.80667.80Answer
  4. D
    863.90863.90

Answer

The final cost of the laptop is $667.80.
The correct answer is found by completing a two-step percentage calculation. First, the 25%25\% discount is applied to the $840\$840 original price (840×0.25=210840 \times 0.25 = 210), yielding a sale price of $630\$630. Then, the 6%6\% sales tax must be calculated on this new sale price (630×0.06=37.80630 \times 0.06 = 37.80) and added to it. Adding the tax to the sale price gives a final total of $667.80\$667.80.

Step-by-Step Solution

1
Calculate the dollar amount of the military discount.
840×0.25=210840 \times 0.25 = 210
To find the discount, multiply the original price by the decimal equivalent of the percentage (25%=0.2525\% = 0.25).
2
Subtract the discount from the original price to find the sale price.
840−210=630840 - 210 = 630
The discount must be subtracted from the original price to determine the amount that will be taxed.
3
Calculate the amount of sales tax on the discounted price.
630×0.06=37.80630 \times 0.06 = 37.80
Sales tax is calculated as a percentage of the final sale price, not the original price.
4
Add the sales tax to the discounted price to find the total final cost.
630+37.80=667.80630 + 37.80 = 667.80
The final amount paid is the sum of the sale price and the calculated tax.

Key Concept

Calculating Percentages of Quantities

Alternative Method

Instead of calculating the discount amount and subtracting, you can determine what percentage of the price you will pay. If there is a 25%25\% discount, you pay 75%75\% of the original price (0.750.75). To include a 6%6\% tax, you multiply by 1.061.06. You can calculate the final price directly as: $840×0.75×1.06=$667.80\$840 \times 0.75 \times 1.06 = \$667.80.
Estimated Time:1m 30s
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Topics

Calculating Percentages of Quantities

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