Question 952010: Can someone please explain to me how to set up the equations for these. Thank you!
A catering service uses the function
[c(x) = 300 + 17x/x] to determine the amount, in dollars, it charges per person for a sit-down dinner, where x is the number of people in attendance.
(a) Find c(75) and explain what it represents.
The company charges $ (Insert answer here )per person to cater a dinner for 75 people.
(b) Find c−1.
c−1 =
(c) Use c−1 to determine how many people attended a dinner for which the cost per person was $19.00.
c−1($19.00) =
people
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A catering service uses the function
[c(x) = (300 + 17x)/x] to determine the amount, in dollars, it charges per person for a sit-down dinner, where x is the number of people in attendance.
(a) Find c(75) and explain what it represents.
c(75) = (300+17*75)/75 = $21
The company charges $21 per person to cater a dinner for 75 people.
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(b) Find c^−1.
Interchange x and y to get::
(300 + 17*y)/y = x
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Solve for y to get :
300+17*c(x) = x*c(x)
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300 + 17y = yx
17y-yx = -300
y(x-17) = 300
y = 300/(x-17)
That is c^-1:::
y is # of people
x is cost per person
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(c) Use c^−1 to determine how many people attended a dinner for which the cost per person was $19.00.
Solve::
y = 300/(x = 17)
y = 300/(19-17)
y = 300/2
y = 150 people
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Cheers,
Stan H.
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