SOLUTION: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
John hosts an art workshop on the weekends. He has an average of 1
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Question 1113247: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
John hosts an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. He estimates that for every $2 increases in the fee, the average number of students reduces by 1.
Complete the equation that models this scenario, where c(x) is the revenue generated and x is the number of $2 fee increases.
c(x) = x2 + x +
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The way you posed this question was confusing. \ =\ x^2\ +\ x\ +\ )
implies that the coefficients on the high order and first-degree terms must be one, which, of course, is impossible. Had you said "find the coefficients for \ =\ ax^2\ +\ bx\ +\ d)
" then it would make sense. And that is the only way that I can make sense of your question so that's what I'm going to show here.
We know that he gets 14 students @ $12 each, so if 
then his revenue is $168. If 
he gets 13 students @ $14 each, so his revenue is $182. And if 
we have 12 @ $16 for $192. Symbolically:
\ =\ a(0)^2\ +\ b(0)\ +\ d\ =\ 168)
\ =\ a(1)^2\ +\ b(1)\ +\ d\ =\ 182)
\ =\ a(2)^2\ +\ b(2)\ +\ d\ =\ 192)
Since the first equation reduces to 
we can reduce the other two equations to:
(1) 
(2) 
From (1):
Substituting into (2)
\ =\ 24)
Substituting back into (1)
And the desired function becomes:
\ =\ -2x^2\ +\ 16x\ +\ 168)
Extra credit: What is the price point to maximize revenue? Hint: What is the 
-coordinate of the vertex of this concave-down parabola?
John
My calculator said it, I believe it, that settles it
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