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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.
The total cost of the ping-pong table is $500.
Each contributor pays an equal share of the total cost.
Therefore, the cost per share, C, can be represented by the function:
C = 500 / x
Jane already has 5 contributors lined up, so the total number of contributors is:
x = 5 + n, where n is the number of new contributors Jane recruits.
To find out how many new contributors Jane must recruit in order for the cost of each share to be $20.00, we need to solve the equation:
20 = 500 / (5 + n)
Solve for 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 $20.00.