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Difficulty: MediumPercentage Change, Markups, and Discounts

A hardware store sells a specific model of commercial power drill. The store sets the regular retail price by applying a 40%40\% markup to the wholesale cost. During a clearance event, the drill is sold at a 20%20\% discount off the regular retail price. If a customer paid $168.00\$168.00 for the drill during the clearance event, what was the store's original wholesale cost for the drill?

  1. A
    $126.00\$126.00
  2. B
    $140.00\$140.00
  3. $150.00\$150.00Answer
  4. D
    $15.00\$15.00

Answer

$150.00\$150.00
To find the original wholesale cost, the percentage changes must be reversed step-by-step. First, find the regular retail price by dividing the sale price by 0.80 (since it reflects a 20% discount). This gives $210.00\$210.00. Then, find the wholesale cost by dividing the regular retail price by 1.40 (since it reflects a 40% markup). This yields the correct wholesale cost of $150.00\$150.00.

Step-by-Step Solution

1
Calculate the regular retail price before the clearance discount.
$168.00÷(1−0.20)=$168.00÷0.80=$210.00\$168.00 \div (1 - 0.20) = \$168.00 \div 0.80 = \$210.00
The clearance price is 80% of the regular retail price, so dividing by 0.80 reverses the discount.
2
Calculate the original wholesale cost using the regular retail price.
$210.00÷(1+0.40)=$210.00÷1.40=$150.00\$210.00 \div (1 + 0.40) = \$210.00 \div 1.40 = \$150.00
The regular retail price is 140% of the wholesale cost, so dividing by 1.40 reverses the initial markup.

Key Concept

To find an original value after successive percentage changes, divide the final amount by the respective percentage multipliers in reverse order.
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Topics

Percentage Change, Markups, and Discounts

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