Question

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.

Answer 1

Call the Fixed cost f.
Call the cost per Person p.
Then Total cost = Fixed cost + (cost per Person)* (Number of People Served)

So T = f + p*n.

If you want to help yourself understand it better,
the total cost depends on how many people are served.
In other words, the total cost is “a function of how many people are served”.

If you think of it in function terminology, you can say T(n) = f + p*n,
where n is the independent variable and T(n) is a function of n.

Anyways, you’re given that T(100) = 750 and T(150) = 1050.
That means that f + p*100 = 750 and that f + p*150 = 1050.

We want to solve this system of equations.
If you haven’t learned how to do that, feel free to ask for clarification.

You can: subtract the first equation from the second to get:
50p = 300, so p = 60.
Then that would mean f + (60)*100 = 750,
so f + 600 = 750, or f = 150.