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A merchant paid $300 for a shipment of x identical

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A merchant paid $300 for a shipment of x identical [#permalink] New post 26 Feb 2006, 10:41
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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Re: Problem Solving Help [#permalink] New post 26 Feb 2006, 11:19
Avis wrote:
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


E.

(300/x+5)(x-2) = 120+300

Instead of solving the equation substitute the answers for x.
Try the easy one e) 30. ((300/30)+5)(30-2)=420
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 [#permalink] New post 26 Feb 2006, 19:04
Average cost of the x calculators = 300/x

Merchant sold (x-2) calculators at (300/x + 5) dollars

Profit

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

Ans E
  [#permalink] 26 Feb 2006, 19:04
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