Question 1092513: The income in dollars for a charity fundraiser can be expressed by 360p-12p^2 where p is the ticket price. What ticket price(s) will result in an income of $0?
Answer by DrSteve(7)   (Show Source):
You can put this solution on YOUR website! This one is a bit more difficult than it looks, but it's totally do-able with the knowledge that you have!
in other words, the income is expressed as the equation, and setting the whole thing to zero and solving for "p" will give the price (p)
you'd have to charge to make zero money on this fundraiser (a really, really bad idea!)
So let's do this!
First, notice that 360 is divisible by 12 and there is a "p" in all parts of the left hand of the equation. So we can factor out -12p to get:
or
this is where having a zero on one side of the equation makes things easy!
divide both sides by -12 to get
there are two ways that that equation can equal zero.
One is if p = 0, as can be seen in:
or if P =30 as in:
so if you charge 0 dollars, it'll result in an income of 0 dollars (which makes sense, when you think about it).
Also if you charge $30 it will result in an income that is exactly zero.
And that is the answer, both 0, and 30!
YAY!
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