Erin is organizing a fundraiser to purchase an air hockey table for her school. The table costs $900.00. Erin is asking for people to contribute to pay an equal share of the cost of the table. She already has seven contributors signed up. a) Write a function that models the cost per share, C, with respect to the number of new contributors, p. (1 point) b) How many new contributors must Erin recruit in order for the cost of each share to be $50? (2 points) (3 points)

Question

Erin is organizing a fundraiser to purchase an air hockey table for her school. The table costs $900.00. Erin is asking for people to contribute to pay an equal share of the cost of the table. She already has seven contributors signed up. a) Write a function that models the cost per share, C, with respect to the number of new contributors, p. (1 point) b) How many new contributors must Erin recruit in order for the cost of each share to be $50? (2 points) (3 points)

Answer 1

a) The function that models the cost per share with respect to the number of new contributors can be calculated as follows:

Let x be the total number of contributors (including the initial seven contributors) and y be the cost per share. If the total cost of the table is $900 and there are x contributors, then the cost per share, y, can be calculated as:

y = Total cost / Total contributors
y = $900 / x

Since Erin already has seven contributors signed up, the number of new contributors is p, so the total number of contributors is x = 7 + p. Therefore, the function that models the cost per share with respect to the number of new contributors is:

C(p) = $900 / (7 + p)

b) To find out how many new contributors Erin must recruit in order for the cost of each share to be $50, we can set the cost per share (C) to $50 and solve for p:

$50 = $900 / (7 + p)
$50 * (7 + p) = $900
350 + 50p = $900
50p = $550
p = 11

Therefore, Erin must recruit 11 new contributors in order for the cost of each share to be $50.