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Difficulty: HardPercentage Change, Markups, and Discounts

An electronics store purchases a computer monitor at wholesale cost. To determine the regular retail price, the store applies a 50%50\% markup to the wholesale cost. During a holiday sale, the monitor is discounted by 30%30\% off the regular retail price. A customer purchases the monitor during the sale and pays a final total of $453.60\$453.60, which includes an 8%8\% sales tax applied to the discounted price. What was the store's original wholesale cost for the monitor?

  1. A
    $240.00\$240.00
  2. B
    $300.00\$300.00
  3. $400.00\$400.00Answer
  4. D
    $350.00\$350.00

Answer

The original wholesale cost was $400.00\$400.00.
The correct wholesale cost is found by working backward from the final paid amount. First, dividing $453.60\$453.60 by 1.081.08 removes the 8%8\% tax, revealing the discounted sale price of $420.00\$420.00. Since this sale price reflects a 30%30\% discount, it is 70%70\% of the retail price; dividing $420.00\$420.00 by 0.700.70 gives the retail price of $600.00\$600.00. Finally, the retail price includes a 50%50\% markup, making it 150%150\% of the wholesale cost. Dividing $600.00\$600.00 by 1.501.50 yields the correct original wholesale cost of $400.00\$400.00.

Step-by-Step Solution

1
Remove the 8%8\% sales tax from the final total to find the discounted sale price.
$453.60÷1.08=$420.00\$453.60 \div 1.08 = \$420.00
The final total includes an 8%8\% tax applied to the sale price, which is mathematically equivalent to multiplying the sale price by 1.081.08.
2
Reverse the 30%30\% discount to determine the regular retail price.
$420.00÷0.70=$600.00\$420.00 \div 0.70 = \$600.00
The sale price represents 70%70\% (100%−30%100\% - 30\%) of the regular retail price.
3
Reverse the 50%50\% markup to find the original wholesale cost.
$600.00÷1.50=$400.00\$600.00 \div 1.50 = \$400.00
The retail price represents a 50%50\% increase over the wholesale cost, equivalent to 150%150\% of the original cost (or multiplying by 1.501.50).

Key Concept

Successive percentage changes and reversing percentages by division.
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Topics

Percentage Change, Markups, and Discounts

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