Question

The projected sales volume of a video game cartridge is given by the function s(p) = 3000 / (2p + 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, 100000 cartridges are sold at 10 dollars per cartridge, how many cartridges will be sold at 20 dollars per cartridge?

Answer 1

Approximately 149,380 cartridges will be sold at $20 per cartridge.

Step-by-step explanation:

To find out how many cartridges will be sold at $20 per cartridge, we can use the given function s(p) = 3000 / (2p + a), where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant.

Given that 100000 cartridges are sold at $10 per cartridge, we can substitute the values into the function:

s(10) = 3000 / (2(10) + a) = 100000

solving for a:

3000 / (20 + a) = 100000

3000 = 100000(20 + a)

3000 = 2000000 + 100000a

-1997000 = 100000a

a = -1997000 / 100000 = -19.97

Now, we can find how many cartridges will be sold at $20 per cartridge:

s(20) = 3000 / (2(20) - 19.97) = 3000 / (40 - 19.97) = 3000 / 20.03 = 149.38

Therefore, approximately 149,380 cartridges will be sold at $20 per cartridge.

Answer 2

Answer: 149 cartridges will be sold at 20 dollars per cartridge.

Step-by-step explanation:

Given: The projected sales volume of a video game cartridge is given by the function
`s(p)=(3000)/(2p+a)`, where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant.

Put s(p)=100000, p= 10, we get

`100000=(3000)/(2(10)+a)\\\\\Rightarrow\ 100=(3)/(20+a)\\\\\Rightarrow\ 100(20+a)=3\\\\\Rightarrow\ 2000+100a=3\\\\\Rightarrow\ 100a=-1997\\\\\Rightarrow\ a=-19.97`

i.e.
`s(p)=(3000)/(2p-19.97)`

Put p=20, we get

`s(20)=(3000)/(2(20)-19.97)\\\\=(3000)/(40-19.97)\\\\=(3000)/(20.03)\approx149`

Hence, 149 cartridges will be sold at 20 dollars per cartridge.