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Difficulty: MediumDiscounts and Sale Prices

An auto repair shop owner orders a bulk supply of replacement brake pads with an original total cost of $800\$800. The automotive parts distributor applies a 15%15\% bulk discount to the order. In addition, the shop receives an extra 5%5\% discount on the reduced price for paying the invoice in full upon delivery.

Determine the shop's final purchase price for the brake pads and the total amount of money saved compared to the original cost.

Answer:The final purchase price is $【646】\$【646】 and the total amount saved is $【154】\$【154】.

Answer

The final purchase price is 646andthetotalamountsavedis646 and the total amount saved is 154.
The correct final price is found by taking 15% off 800toget800 to get 680, then taking 5% off 680toarriveat680 to arrive at 646. The total savings is the sum of both discounts (120+120 + 34 = $154).

Step-by-Step Solution

1
Calculate the amount of the 15% bulk discount.
$800×0.15=$120\$800 \times 0.15 = \$120
To find the savings provided by the initial distributor discount.
2
Calculate the intermediate price after the first discount.
$800−$120=$680\$800 - \$120 = \$680
The subsequent 5% discount must be applied to this reduced price, not the original price.
3
Calculate the amount of the 5% payment discount.
$680×0.05=$34\$680 \times 0.05 = \$34
To determine the additional savings from paying the invoice in full upon delivery.
4
Calculate the final purchase price.
$680−$34=$646\$680 - \$34 = \$646
This is the final amount the shop must pay after all successive discounts have been applied.
5
Calculate the total amount saved.
$120+$34=$154\$120 + \$34 = \$154
To find the complete difference between the original cost and the final price.

Key Concept

Successive discounts must be calculated sequentially on the new reduced price at each step, rather than adding the percentages together.
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Topics

Discounts and Sale Prices

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