题目信息
A merchant paid $300 for a shipment of x identical calculators. The merchant used two 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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正确答案：
E:30
Algebra Second-degree equations
The merchant paid $300 for a shipment of x calculators, so the average cost, in dollars, per calculator was
. The merchant sold (x – 2) of them at the price of 5 + 
dollars each, for a total revenue of (x – 2)
dollars, which was 120 + 300 = 420. Manipulating the equation (x – 2)
= 420 gives x 2 – 26x – 120 = 0 or (x – 30)(x + 4) = 0, which can be solved by factoring. It follows that there were 30 calculators in the shipment.
The correct answer is E.
The merchant paid $300 for a shipment of x calculators, so the average cost, in dollars, per calculator was
. The merchant sold (x – 2) of them at the price of 5 + dollars each, for a total revenue of (x – 2) dollars, which was 120 + 300 = 420. Manipulating the equation (x – 2) = 420 gives x 2 – 26x – 120 = 0 or (x – 30)(x + 4) = 0, which can be solved by factoring. It follows that there were 30 calculators in the shipment.The correct answer is E.
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