Question

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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 new contributors, n? How many new contributors must Jane recruit in order for the cost of each share to be $20.00?

Answer 1

Let x be the total number of shares needed to buy the table, so x = 500

Let y be the total number of contributors lined up already, who will pay for 2 shares each, so y = 2*5 = 10

The number of new contributors needed would be x/20 - y to bring the total number of contributors to x/20, thus the number of new contributors is (500/20) - 10 = 25 - 10 = 15

Function C(n) = x / (y + 2n)
Substitute x = 500, y = 10:
C(n) = 500/(10+2n)

To make the cost per share $20:
C(n) = 500/(10 + 2n) = 20
500 = 20(10 + 2n)
500 = 200 + 40n
300 = 40n
n = 7.5

Jane must recruit 8 new contributors to make the cost of each share $20.