• anonymous
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.
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • schrodinger
I got my questions answered at in under 10 minutes. Go to now for free help!
  • anonymous
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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.