I have a 3 part problem that isn't adding up and i need help please

Question

You plan to join a gym near your house. Cyber Fitness will charge you $200/year plus and additional $4 per fitness class you attend. Sly's Gym will charge $300/year but only $2 per fitness class.

1. Write a model representing the cost of Cyber Fitness, C_{c, if you attend x fitness classes.}

2. Write a model representing the cost of Sly's Gym, C_{s, if you atten}x fitness classes.

3. Find the number of fitness class(es) you would need to attend for the cost of both gyms to be the same. What would be the cost of using either gym at that point. Show all work. Find your answer algebraically. Write a sentence to explain your answer.

Answer 1

1. C_c = 200 + 4x 

2. C_s = 300 + 2x

 

3. We set these two equations equal to each other to each other to solve for x. This will tell us how many fitness classes are needed to have the two prices be equal.

 

200 + 4x = 300 + 2x

 

4x - 2x = 300 - 200

2x = 100

X = 50

So after 50 classes, the costs will be equal. We can check this by plugging 50 into both equations, and this will also answer the question of how much the gym memberships would cost.

 

C_c = 200 + 4(50)  = 200 + 200 = 400

C_s = 300 + 2(50) = 300 + 100 = 400

 

So they would both cost $400 dollars at the point where they are equal.