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Difficulty: MediumPercentage Change, Markups, and Discounts

An automotive dealership initially offers a customer a trade-in value of $4,500.00\$4,500.00 for their used vehicle. After a mechanical inspection reveals worn brake pads and a minor oil leak, the dealership decreases this initial offer by 12%12\%. To help close the deal on a new vehicle, the sales manager then approves a 5%5\% increase on the revised trade-in offer. What is the final trade-in value offered to the customer?

Answer: 4158 $

Answer

4158
The correct answer is found by taking the initial amount of 4,500,decreasingitby124,500, decreasing it by 12% to find the intermediate value of 3,960, and then increasing that intermediate value by 5% to arrive at the final value of $4,158.

Step-by-Step Solution

1
Calculate the dollar amount of the 12% decrease.
$4,500×0.12=$540\$4,500 \times 0.12 = \$540
The initial offer is reduced by 12% due to mechanical issues found during the inspection.
2
Determine the revised trade-in offer after the initial decrease.
$4,500−$540=$3,960\$4,500 - \$540 = \$3,960
Subtracting the penalty from the original amount establishes the new base value for the next percentage change.
3
Calculate the dollar amount of the 5% increase.
$3,960×0.05=$198\$3,960 \times 0.05 = \$198
The manager's 5% increase applies specifically to the revised offer, not the original amount.
4
Calculate the final trade-in value.
$3,960+$198=$4,158\$3,960 + \$198 = \$4,158
Adding the approved increase to the revised offer provides the final amount offered to the customer.

Key Concept

Successive percentage changes
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Topics

Percentage Change, Markups, and Discounts

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