SOLUTION: This word problem pertains to "REVENUE". The demand for a certain product is given by p=26-.01x, where x is the number of units sold per month and p is the price, in dollars, at

Question 288313: This word problem pertains to "REVENUE".
The demand for a certain product is given by p=26-.01x, where x is the number of units sold per month and p is the price, in dollars, at which each item is sold. The monthly revenue is given by R=xp. What number of items sold produces a monthly revenue of $16,500.
I was on a roll for a while, but now I'm stuck again. I missed class last week (job sent me out of country) and I seriously don't even know where to begin with this. The book doesn't clearly state what I should do with this problem (like if I should use the quadratic formula or something along those lines) and I can't find any examples similar to it to try and work with.
I was thinking something like:
$16,500=x(26-.01x)
so, $16,500=26x-2.86x^2
then, divide the left side by 2?
so, $16,500=13x-1.43x
then, $16,500=11.57x
Okay, so then it would be $1,426.10=x?
This doesn't seem right.
Could somebody please explain how I am supposed to find the solution for this type of problem?
Thanks! Any help is appreciated!
Answer by jaydducote(11) (Show Source): You can put this solution on YOUR website!
Good start, but not quite:
$16,500=x(26-.01x) is exactly right.
However, you now need to distribute only the x that is by itself, so:
16,500=26x-.01x^2
From here it you will need to use the quadratic equation or find some way to break it down. The problem will actually generate two solutions. I would move everything to left side:
.01x^2-26x+16500=0
Now,
This leaves us with x=1100 and 1500. So at 1100 and 1500 units sold, we will get a R of $16,500.
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