# Math Help - [SOLVED] Question about some site's question/answer solution with given function

1. ## [SOLVED] Question about some site's question/answer solution with given function

This is the problem on the other site, though I have a question about how/why they did what they did(for the solution).

Here's the question:
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"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;
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?"
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So, I am guessing we're trying to find "s", but instead of using "10 = p", we're using "20 = p".

I assumed "s(p) = 3000 / 2p + a", plugged in would be look like this:
100(10) = 3000 / 2(10) + a

That's not what they did for the solution, they did this
100 = 3000 / 2(10) + a
They took out the (p) on left side of the function.
Here's their entire solution btw.

Question:
Why did they not include the (p) on the left side of the question, to make it "100(10) = 3000 / 2(10) + a" but instead did "100 = 3000 / 2(10) + a", when they gave the function ?
Error or mistake?
Or is that how you're supposed to do it?

2. Are you familiar with functions?

s(p) is a notation. The letter of the function is s. When it says s(10), that means: "plug in the 10 in every variable p".

They said that s is the number of cartridges sold (in thousands) and p is the price per cartridge. They also said that at the price \$10, 100000 cartridges were sold.

So, $s(10) = \frac{100000}{1000} = 100$

To solve this question, you must find the constant a using the given value of s(10), then find s(20).