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 w

Question 243272: 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 with be $1050.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
To figure the cost/person, look at the change in cost divided by the change in attendance.
For 100 students, cost = $750.
For 150 students, cost = $1050.
Change in cost = $300
Change in students = 50
Cost per additional student = 300/50 = $6
...
Assuming the costs are linear, then the price charged for 100 students reflects the cost per student + a 'fixed cost' that applies to the order as a whole.
100 * 6 = $600, so the fixed cost is 750-600 = 150.
...
We can check this notion by substituting in the other equation.
Does 150*6 + 150 = 1050?
150*6=900
900+150 = 1050.
Yes.
...
We can express this relationship by the equation:
y = mx + b
where
y = total cost
m = $6 per student
x = number of students
b = fixed costs = 150
y = 6x + 150
...
Done
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