SOLUTION: A restaurant has some fixed operating costs and some that vary with the number of people in attendance. If 4000 people visit a restaurant in one month, the operating costs are $13

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Question 416185: A restaurant has some fixed operating costs and some that vary with the number of people in attendance. If 4000 people visit a restaurant in one month, the operating costs are $1300. If 2800 people visit the restaurant the operating costs are $970. What would be the operating costs for this restaurant in a month where only 1500 people visit the restaurant?

I can't even begin to put this in a f(x) type problem. I was trying to come up with possible fixed costs that would work first in my head (for example $300 so then $1000 for 4000 people and $700 for 2800 people but the $970 is off. I am stuck!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A restaurant has some fixed operating costs and some that vary with the number of people in attendance.
If 4000 people visit a restaurant in one month, the operating costs are $1300.
If 2800 people visit the restaurant the operating costs are $970.
What would be the operating costs for this restaurant in a month where only 1500 people visit the restaurant?
:
Let x = cost per person
Let f = fixed operating costs
:
write a cost equation for each scenario
4000x + f = 1300
2800x + f = 970
-------------------subtraction eliminates f, find n
1200x = 330;
x = 330%2F1200
x = $.275 cost per person
:
Find the fixed cost using the 1st equation
4000(.275) + f = 1300
1100 + f = 1300
f = 1300 - 1100
f = $200 is the fixed cost
:
Check the n and f values in the 2nd equation
.275(2800) + 200 =
770 + 200 = 970; confirms our solution
:
" What would be the operating costs for this restaurant in a month where only 1500 people visit the restaurant?"
.275(1500) + 200 =
412.5 + 200 = $612.50, cost for 1500 people