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 *n*th 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 for a member to 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 (2)
a. 550-(3x75)=325 b. The 9th member may join free as 550-(75x8)=-50 and as I imagine the gym will not pay the customer money they should have a free membership but only after the 9th person. c. $25, 550-(75x7)=25 therefore the 8th person pays $25 for their membership.
The fourth member pays $325. The 8th member theoretically joins for free, while the 8th member pays the lowest fee of $25. The pricing structure indicates that costs decrease as more family members join, potentially leading to a free membership situation.
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