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a video game cartridge

by sanju09 » Wed Jul 07, 2010 4:45 am
The projected sales volume of a video game cartridge is given by the function s (p) = 3000/ (2 p + a) where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant. If according to the projections, 100,000 cartridges are sold at $10 per cartridge, how many cartridges will be sold at $20 per cartridge?
(A) 20,000
(B) 50,000
(C) 60,000
(D) 150,000
(E) 200,000
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by kmittal82 » Wed Jul 07, 2010 5:01 am
100,000 = 100 thousand cartridges.

Acc. to the given info, 100,000 cartridges are sold at $10 per cartridge:

100 = 3000 /(2x10 + a)
=> a = 10

Thus, at p = 20, s(p) = 3000/(2x20 + 10) = 60 => 60,000

Hence, (C) is the right answer
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by Rahul@gurome » Wed Jul 07, 2010 5:02 am
Here, s = 100 (it is given s is the number of cartridges sold, in thousands and $10 is the price per cartridge)
p = 10
100 = 3000/(20 + a) implies 2000 + 100a = 3000 or a = 10
So, s(p) = 3000/ (2p + 10) implies s(20) = 3000/ (2(20 )+ 10) = 3000/50 = 60
Therefore, 60,000 cartridges will be sold at $20 per cartridge.

The correct answer is (C).
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by AntonS » Fri Dec 13, 2013 7:09 am
Questions about this question are all over the web. This one seems to be the most edified discussion, so I'll post my inquiry here:

I want to understand how the left side of the equation -- which is shown as s(p) can be 100.

The problem states that s is the number of cartridges sold, IN THOUSANDS, and that p is the price per cartridge.

Therefore s=100 and p=10 yielding a left side of 1000 -- not 100 (at least to me).

Someone. Please. Tell me what I'm missing. What in the symbology suggests that the expression "s(p)" is not a multiplication function??
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