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Senior Manager
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A merchant paid $300 for a shipment of x identical calculato [#permalink]
 03 Jun 2005, 01:55
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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. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
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Senior Manager
Joined: 17 May 2005
Posts: 273
Location: Auckland, New Zealand
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The total amount paid was $300 for x calculators.
The amount paid for each calculator = 300/x
The amount each calculator was sold for = 300/x + 5 = (300+5x)/x
The number of calculators sold = (x-2)
Revenue earned = 300 + 120 = 420
Revenue earned = number of calculators sold * selling price of each calculator.
Therefore:
[(300+5x)/x]*(x-2) = 420
[(300+5x)(x-2)]/x=420
(300+5x)(x-2)=420x
300x+5x^2-600-10x=420x
5x^2-130x-600=0
5(x^2-26x-120)=0
x^2 - 26x - 120 = 0
(x - 30) (x - 4) = 0
x = 30 or -4
as it can't be -4, answer has to be 30.
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