Question 818234: Hello can someone please help with this word problem.
A certain bakery has found that the daily demand for blueberry muffins is 3200/p, where p is the price on a muffin in cents. The daily support is 3p-200. Find the price at which supply and demand are equal.
I get 35 and my answer key is saying .80 so I was hoping to get some help here
3200/p = 3p-200
then I multiplied by p
which gave me 3200=3p^2-200p
in standard form
3p^2-200p-3200=
this was my start and in the end I ended up with 35. Is my start wrong?
Thank you! :-)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Your start is right, you must have made some calculation error.
If supply is  and demand is 
 is the right equation to make supply equal demand.
Also, from you get 
and  as you meant to write.
I see 3 ways to solve that equation:
factoring, completing the square, and using the quadratic formula.
Since I had my calculator next to me,
I found it easier to use the quadratic formula,
which says that the solutions to  can be calculated as
In your case,  ,  , and  , so
The solution with the minus sign, 
does not make sense, because the price has to be a positive number of cents.
The other solution is
 ,
meaning that pricing each muffin at 80 cents will make supply meet demand.
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