SOLUTION: A caterer charges a fixed cost for preparing dinner plus an additional cost for each person served. You know the cost for 100 students will be $750 and the cost for 150 students wi

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Question 252699: A caterer charges a fixed cost for preparing dinner plus an additional cost for each person served. You know the cost for 100 students will be $750 and the cost for 150 students will be $1050. Find the caterer's fixed cost and the cost per student served.
Found 2 solutions by drk, richwmiller:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let the cost function be:
(i) C = mP + b
Where C = total cost, P = number of people, b = fixed cost, and m = cost per person.
we actually have coordinates: (100,750) and (150,1050). We put those into (i).
(ii) 750 = 100m + b
(iii) 1050 = 150m + b.
At this point, multiply (ii) by -1 and add down.
(iv) 300 = 50m
m = 6: Cost per student
Now we put 6 back into (ii) for m to find b.
(v) 750 = 100(6) + b
b = 150: fixed cost
C = 6P + 150.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
100 at 750
150 at 1050
so the last 50 cost 300
300/50=6 dollars each
100*6=600
750-600=150
so the caterer charges 150 plus 6 dollars per person
check
150+150*6=50+1000
x+100y=750
x+150y=1050
subtract second from first
50y=300
y=6
x+6*100=750
x=150