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 m
ember 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.
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.
