Question

Sarah belongs to a gym and health spa that is conveniently located between her home and her job. It is one of the nicer gyms in town, and Sarah pays $90 a month for membership. Sarah works out three times a week regularly. While she was gelling off the treadmill one day, one of the club's personal trainers came by to talk and offered to plan a routine for Sarah that would help her train for an upcoming marathon. The trainer had noticed that Sarah came in regularly, and she commented that most members don't have the self-control to do that. In fact, she explained that there was a study of in Boston area gyms showing that members went gym only about five times per month. The study also found that people who choose a pay-per-visit membership spend less money than people who choose a monthly or annual membership fee.

1. At Sarah's club, the pay-per-visit fee is $5 per day. Would Sarah save money paying per visit? Assume that a month has 4.3 weeks. What percentage of her monthly $90 fee would she spend if she paid on a per-visit basis?
2. If Sarah goes to the gym three times per week, what percent of days of the year does she use the gym? Round to the nearest percent. 3. If Sarah went to the gym every day, how much would she pay per day on the monthly payment plan? Assume 30 days in a month. If she went every day and paid $5 per day, how much would she be spending per month? What percent more is this compared to the $90 monthly rate rounded to the nearest percent?

Answer 1

1) She would save money if she paid per-visit. She would only pay %72 of what she pays monthly

2) She goes to the gym %43 of the days of the year

3) If she goes every day to the gym, she would spend $150 per month if she paid per-visit, that is %67 more than the $90 monthly fee

Explanation:

1) She goes to the gym 3 times per week, so she goes 3*4.3 = 12.9 times per month. Thus, if she were to pay only $5 per day instead of a monthly membership, she would spend 5*12.9 = $64.5 per month.

Therefore, she would save money if she paid on a per visit basis, by using a rule of three, we can conclude that she would spend only 64.5*100/90 = %72 of her monthly $90 fee.

2) If she goes 3 times per week, she is going 3 days out of 7, thus, she is going 3*100/7 = %43 days of the year.

3) If a month has 30 days, then she would spend 30*5 = $150 if she paid per-visit and she went to the gym every day. That is $60 more than the $90 she spends for her monthly membership, in other words, it is 60*100/90 = %67 more than the %90 monthly rate.