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Retired Moderator
Joined: 16 Apr 2020
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WE:Education (Education)
A merchant paid $300 for a shipment of x identical calculators.
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02 Aug 2021, 22:16
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.
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
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
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
A merchant paid $300 for a shipment of x identical calculators.
[#permalink]
03 Aug 2021, 19:58
03 Aug 2021, 19:58
1
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
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
Re: A merchant paid $300 for a shipment of x identical calculators.
[#permalink]
23 Apr 2024, 05:50
23 Apr 2024, 05:50
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