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,, 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 and y be the cost per share.
The total cost of the ping-pong table is $500. If each contributor pays an equal share, then the cost per share is given by:
y = 500 / x
If Jane already has 5 contributors and is looking for n new contributors, the total number of contributors will be x = 5 + n.
Substitute x = 5 + n into the equation for y:
y = 500 / (5 + n)
To find out how many new contributors Jane must recruit in order for the cost of each share to be $20.00, set y equal to 20 and 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 $20.00.