Question

Amir Najjar did research on the Internet to find the dealer's cost of a new car he wanted to purchase. He found that the dealer's cost of the base price was $15,455.40 and cost of the options was$585.00. The dealer will pass the $675 destination charge on to the consumer. If the dealer's cost is 85% of the base and 82% of the options, what is the car's sticker price?

Answer 1

$19,571.24

Explanation:

You want the sticker price of a car if the dealer's costs for base price, options, and destination charge are $15,455.40, $585.00, and $675, respectively, and those represent 85%, 82%, and 100% of the prices shown on the sticker, respectively.

Sticker price

We are told that the dealer cost (d) is some percentage ℗ of the sticker price (s) for each of the line items:

d = p·s

Then the sticker price of each line item will be ...

s = d/p

Line items

The sum of the sticker prices for the three line items is ...

• base price: 15,455.40/0.85 = 18,182.824
• options: 585/0.82 = 713.415
• destination charge = 675/1.00 = 675.000

The sum is then ...

18,182.824 +713.415 +675.000 = 19571.239 ≈ 19571.24

The car's sticker price is $19,571.24.

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Additional comment

You may have noticed that the line item prices have fractions of cents that will not cause their values to be rounded up. However, when those fractions are totaled, the sum can be rounded up. The value shown here may be $0.01 more than the value you're expected to report due to the fact that we didn't round until the end of the calculation.

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