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Difficulty: HardPercentage Change, Markups, and Discounts

A local boutique acquires a designer winter coat from a distributor for a wholesale cost of $125.00\$125.00. The store manager applies a 60%60\% markup to establish the regular retail price. Later in the season, the coat is moved to the clearance rack, receiving a 30%30\% discount off its regular retail price. A shopper buys the coat using a loyalty reward that takes an additional 10%10\% off the clearance price. If a 5%5\% sales tax is calculated on the final discounted price, what is the total amount the shopper pays at the register?

  1. $132.30\$132.30Answer
  2. B
    $136.00\$136.00
  3. C
    $157.50\$157.50
  4. D
    $168.00\$168.00

Answer

The shopper pays a total of $132.30\$132.30 at the register.
The total amount is found by applying each percentage change successively to the new amount from the previous step. First, the 60% markup sets the price at 200.00.The30200.00. The 30% clearance discount reduces this to 140.00. The 10% loyalty discount further reduces it to 126.00.Finally,a5126.00. Finally, a 5% tax on the 126.00 final price adds 6.30,resultinginatotalof6.30, resulting in a total of 132.30.

Step-by-Step Solution

1
Calculate the regular retail price by applying the 60%60\% markup to the wholesale cost.
$125.00×1.60=$200.00\$125.00 \times 1.60 = \$200.00
The markup increases the base cost to establish the starting retail price.
2
Calculate the clearance price by applying the 30%30\% discount to the regular retail price.
$200.00×(1−0.30)=$140.00\$200.00 \times (1 - 0.30) = \$140.00
The first discount is taken from the current retail price, not the wholesale cost.
3
Calculate the final item price by applying the 10%10\% loyalty discount to the clearance price.
$140.00×(1−0.10)=$126.00\$140.00 \times (1 - 0.10) = \$126.00
Successive discounts must be applied sequentially to the newly discounted price.
4
Calculate the total amount paid by adding the 5%5\% sales tax to the final item price.
$126.00×1.05=$132.30\$126.00 \times 1.05 = \$132.30
Sales tax is calculated strictly on the final discounted price of the item.

Key Concept

Calculating successive percentages for markups, discounts, and taxes sequentially based on the updated price at each step.
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Topics

Percentage Change, Markups, and Discounts

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