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A merchant paid $300 for a shipment of x identical calculators.

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KarunMendiratta
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A merchant paid $300 for a shipment of x identical calculators. [#permalink] New post   02 Aug 2021, 22:16
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A merchant paid $300 for a shipment of \(x\) identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the \(x\) calculators. The total revenue from the sale of the calculators was $120 more than the cost of the shipment.

Quantity A
Quantity B
Number of calculators sold in the shipment
30


A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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B
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KarunMendiratta
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A merchant paid $300 for a shipment of x identical calculators. [#permalink] New post   03 Aug 2021, 19:58
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Explanation:

Average of \(x\) calculators = \(\frac{300}{x}\)

Calculators sold = \(x-2\)

Revenue = \((x-2)[\frac{300}{x} + 5] = 300 + 120\)

\((x-2)(300+5x) = 420x\)
\(300x + 5x^2 - 600 - 10x = 420x\)
\(5x^2 - 130x - 600 = 0\)
\(x^2 - 26x - 120 = 0\)
\((x-30)(x+4) = 0\)
\(x = 30\)

Col. A: \(x-2 = 28\)
Col. B: \(30\)

Hence, option B
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A merchant paid $300 for a shipment of x identical calculators. [#permalink] New post   16 Oct 2025, 03:32
The wording is confusing, it seems quantity A refers to the first shipment which would be 30.
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A merchant paid $300 for a shipment of x identical calculators. [#permalink]
16 Oct 2025, 03:32
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