Question

Tom wants to join a gym. Gym A charges a $150 membership fee plus $50 per month. Gym B charges a membership fee plus $75 per month. Write and graph a system of equations to determine when the cost at both gyms is the same.

Answer 1

To determine when the cost at both gyms is the same, we can write a system of equations and solve for the number of months. The cost at Gym A can be represented as A = 150 + 50m, and the cost at Gym B can be represented as B = x + 75m. By setting these equations equal to each other and solving for m, we find that the cost will be the same after 6 months.

Step-by-step explanation:

To write a system of equations to determine when the cost at both gyms is the same, let's denote the number of months as 'm'.

For Gym A, the cost can be represented as:
A = 150 + 50m

For Gym B, the cost can be represented as:
B = x + 75m

To find when the cost is the same at both gyms, we need to set the equations equal to each other and solve for 'm':
150 + 50m = x + 75m

Simplifying the equation:
150 = 25m

Dividing both sides by 25:
6 = m

So, the cost at both gyms will be the same after 6 months.