math question algebra

Question

An exercise club offers three payment plans for aerobics classes. Plan A charges $6 per class plus a one-time membership fee of $35. Plan B charges $5 per class plus a one-time membership fee of $50. Plan C offers unlimited aerobic classes for a one-time membership fee of $149.

Part A: Write and solve an inequality to find how many classes you would have to attend for Plan A to be a better value than Plan B.

Part B: Write and solve an inequality to find how many classes you would have to attend for Plan A to be a better value than Plan C.

Part C: The club reduces the cost of Plan C to $100. If you attend 15 classes, which plan is now the best value?

Answer 1

A=35+6c where c= number of classes, A,B,C= total cost

B=50+5c

C=149+(0)c = 149

Plan A is less costly than Plan B if 35+6c<50+5c

c<50-35=15

c<15

if the number of classes is less than 15, Plan A is cheaper

both are less expensive than Plan C for c<15

A=35+6(15)=125 = B=50+5(15) =50+75 =125 < 149

IF plan C's cost is reducted to 100

A is less costly than C if 35+6c<100

6c<100-35 = 65

c<65/6= 10 5/6

if the number of classes is less than 11, Plan A costs less than Plan C

if you buy 15 classes, Plans A and B cost the same and each is more expensive than Plan C

A=35+6(15) =35+90=125

B=50+5(15) = 50+75 = 125

C = 100