A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40

for 3 months. You write two equations in the form of y = kx to try and figure out which membership
would be cheaper for a year. What is the value of k for the cheaper membership?

1 answer

To determine the cheaper membership for a year, we need to compare the cost of 12 months of membership at both Gym A and Gym B.

For Gym A, the cost for 5 months is $50. We can set up the equation as follows:

y = kx
50 = k(5)

Simplifying, we have:
50 = 5k

Dividing both sides by 5, we find:
k = 10

So, the value of k for Gym A is 10.

For Gym B, the cost for 3 months is $40. Setting up the equation:

y = kx
40 = k(3)

Simplifying, we have:
40 = 3k

Dividing both sides by 3, we find:
k = 40/3

The value of k for Gym B is 40/3.

To determine which membership is cheaper for a year, we need to compare the cost of 12 months of membership for both gyms. We'll multiply the value of k by 12 for each gym:

For Gym A:
12 * k = 12 * 10 = 120

For Gym B:
12 * k = 12 * (40/3)

To compare the value of k for the cheaper membership, we need to find the smaller value between 120 and 12 * (40/3) = 160.

Since 120 is smaller than 160, the value of k for the cheaper membership is 10.