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Difficulty: MediumPercentage Change, Markups, and Discounts

A building contractor purchases a shipment of lumber with a regular retail price of $800.00\$800.00. The supplier offers a 15%15\% trade discount for professional contractors. After the discount is applied, a 6%6\% sales tax is added to the purchase. What is the final total cost of the lumber?

  1. A
    $728.00\$728.00
  2. B
    $832.10\$832.10
  3. C
    $1,088.00\$1,088.00
  4. $720.80\$720.80Answer

Answer

The correct answer is $720.80\$720.80.
The correct answer is found by taking the multi-step percentage changes in order. First, find the 15%15\% discount on the regular price: 0.15×$800.00=$120.000.15 \times \$800.00 = \$120.00. Subtract this from the original price to get the discounted price: $800.00−$120.00=$680.00\$800.00 - \$120.00 = \$680.00. Next, calculate the 6%6\% sales tax on this new subtotal: 0.06×$680.00=$40.800.06 \times \$680.00 = \$40.80. Finally, add the sales tax to the discounted price: $680.00+$40.80=$720.80\$680.00 + \$40.80 = \$720.80.

Step-by-Step Solution

1
Calculate the discount amount.
15%15\% of $800.00\$800.00 is $120.00\$120.00.
The trade discount is a percentage reduction based on the regular retail price.
2
Determine the discounted price.
$800.00−$120.00=$680.00\$800.00 - \$120.00 = \$680.00.
Subtracting the discount from the original price gives the subtotal before tax.
3
Calculate the sales tax.
6%6\% of $680.00\$680.00 is $40.80\$40.80.
Sales tax is applied to the discounted price, not the original retail price.
4
Find the final total cost.
$680.00+$40.80=$720.80\$680.00 + \$40.80 = \$720.80.
Adding the calculated sales tax to the discounted subtotal yields the final amount paid.

Key Concept

Calculating successive percentage changes (a discount followed by a tax) on a principal amount.
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Topics

Percentage Change, Markups, and Discounts

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