Question

The gym offers a discount when more than one member of the family joins. The first member (n=0) pays $550 per year. The second member to join (n=1) gets a discount of $75 per year. The third member (n=2) gets an additional $75 discount. The price for the nth member is given by 550+(-75n).

a. What is the price for the fourth member to join (n=3)?

b. For a large family, is it possible that member would join for free? If so, which member would it be? Explain your reasoning.

c. Other than $0, what is the lowest amount that a member would pay to join? Which member would it be? Explain your reasoning.

Answer 1

a. If we subtract 75 from 550 twice, we get 400, which is the third member to join. Subtract 75 from 400, we get $325, the fourth member to join.

b. It is not possible that a member would join for free if it was a large family. 75 does not fit into 550 evenly. You can prove this by solving the expression 550÷75.

c. The lowest amount that a member would pay to join is $25.00. It would be the 7th member.