Question

[Honors Algebra II] Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $500. Jane is asking contributors to pay for an equal share of the cost of the table. She already has five contributors lined up who have offered to pay for two shares each. What function models the cost per share (C) with respect to the number of contributors (n)? How many contributors must Jane recruit in order for the cost of each share to be $20.00?

Answer 1

This is tricky... The 5 contributors who have offered to pay for two shares each, I guess that means they pay twice as much as any additional contributors?

Answer 2

Yes, I believe so. It is really confusing, but that's what I got out of it as well.

Answer 3

OK well n=0, no extra contributors, C=500/10, since there are 10 shares being payed for. For each n that is added, you add 1 to the denominator. For example if there are 2 contributors, then you do 500/12, since there are the 10 shares from the original 5 contributors and 2 from the new contributors. So the rule is

C= 500/(10+n)

Make sense?

Answer 4

Yes, that makes sense.

Answer 5

Do you know how to solve for when the cost is 20 now?

Answer 6

I'm afraid not. Could you explain, please?

Answer 7

C= 500/(10+n)

You want cost to be 20 aka C=20 so:

20=500/(10+n)

Solve for n :)

Answer 8

Ah, I see. So n = 15. Thank you!

Answer 9

You're welcome!