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Jane is organizing a fundraiser to buy a ping-pong table for the community center. The table costs $500.00. Jane is asking contributors to pay for an equal share of the cost of the table. She already has five contributors lined up. 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?
Let x be the total number of contributors, including the initial five. The total cost of the ping-pong table is $500.
Therefore, the initial cost per share is:
C(x) = 500 / x
Now, Jane is looking for the cost per share to be $20, so we set up the equation:
20 = 500 / (5 + n)
Solve for n:
20 = 500 / (5 + n)
20(5 + n) = 500
100 + 20n = 500
20n = 400
n = 20
Therefore, Jane must recruit 20 new contributors in order for the cost of each share to be $20.