Thread: [SOLVED] Finding the Break Even Equation

I'm not sure where to start on this question. Here's the scenario:

"You are hosting a convention for a charitable organization. You pay a rental fee of $22,900 for the convention center, plus you pay the caterer $14 for each person who attends the convention. Suppose you just want to break even."

The question I'm stuck on is:

(a) Use a formula to express the amount you should charge per ticket as a function of the number of people attending. (Let C be the amount charged per ticket (in dollars) and n the number of people attending.)

I know I can figure out the other parts (b-graph formula (a), c-find how many must attend if ticket price is $47). I'm just stuck on (a). Any help is appreciated!

Originally Posted by bpdude

I'm not sure where to start on this question. Here's the scenario:

"You are hosting a convention for a charitable organization. You pay a rental fee of $22,900 for the convention center, plus you pay the caterer $14 for each person who attends the convention.
Suppose you just want to break even."

The question I'm stuck on is:

(a) Use a formula to express the amount you should charge per ticket as a function of the number of people attending. (Let C be the amount charged per ticket (in dollars) and n the number of people attending.)

I know I can figure out the other parts (b-graph formula (a), c-find how many must attend if ticket price is $47). I'm just stuck on (a). Any help is appreciated!

Let n be the number of people who attend. Then your cost will be 22900+ 14n. If you charge each of those people C dollars, then you will bring in Cn dollars. You will "break even" if those are the money you bring in equals the cost. Set 22900+ 14n= Cn and solve for C as a function of n.

Ok, so would it be:

(22900/n)+13n=C?

Never mind, I got it. It was (22900/n)+14=C (thought that when you divide, you subtracted one from the numerator when dealing with variables)

Thank you for your help, HallsofIvy!