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A merchant purchased a jacket for $60

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A merchant purchased a jacket for $60

by BTGmoderatorDC » Mon Jan 22, 2018 5:38 am
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant's gross profit on this sale?

(A) $0
(B) $3
(C) $4
(D) $12
(E) $15

Can some experts show me the best solution in this problem?

OA C
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by [email protected] » Mon Jan 22, 2018 2:11 pm
Hi lheiannie07,

We're told that a merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. We're asked for the merchant's gross profit on this sale. Here's how you can use a bit of Algebra to answer this question:

To start, we need to determine the original selling price. The original markup equals 25% of the selling price...

Purchase Price + Markup = Selling Price
$60 + .25X = X
$60 = .75X
$60 = (3/4)X
($60)(4/3) = X
$240/3 = $80 = X

Thus, the original sell price = $80. Reducing that price by 20% gives us...

$80 - (.2)($80) = 80 - 16 = $64

Sine the discounted sale price is $64, the merchant's gross profit was $64 - $60 = $4.

Final Answer: C

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by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:07 am
lheiannie07 wrote:A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant's gross profit on this sale?

(A) $0
(B) $3
(C) $4
(D) $12
(E) $15
We are given that a jacket was purchased for 60 dollars. The jacket was sold for a price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. We can let the selling price = p, and thus the selling price is 60 + 0.25p. We can create the following equation and solve for p:

p = 60 + 0.25p

Multiply the equation by 4, we have:

4p = 240 + p

3p = 240

p = 80

Since the selling price was then discounted 20%, the discounted price was:

0.8(80) = 64

Thus, the profit on the sale was 64 - 60 = $4.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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