The projected sales volume of a video game cartridge is given by the function 
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?
We are told that and we are also told that if the cartridge sells for $10 each, the projected sales is 100,000. So we can plug those numbers in to create the following equation:
100 = 3000/2(10) + a (Remember that s(p) is measured in thousands. So it should be 100 here, not 100,000.)
We have to multiply both sides by 2(10) + a, or 20 + a. That gives you 100 (20 + a) = 3000. Now we solve for a.
2000 + 100a = 3000
100a = 1000
a = 10
We are told that a is a constant. So now all we have to do is figure out what the projected sales are if the item costs $20 rather than $10.
So we plug in and get
s(20) = 3000/2(20) + 10
s(20) = 3000/50
s(20) = 60
But, remember, s(p) is the number of sales in the thousands. So the answer is (C) 60,000.
