A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street cost $40 for 3 months you write 2 equations in the form of y = kx to try and figure out which membership will be cheaper for a year what is the value of k for the cheaper membership

Answer 1

Let's represent the cost of a Gym A membership as y₁ and the number of months as x₁, and represent the cost of a Gym B membership as y₂ and the number of months as x₂.

From the given information, we have the following equations:
For Gym A:
y₁ = 50x₁

For Gym B:
y₂ = 40x₂

To determine which membership will be cheaper for a year, we need to find the value of k (the rate of change of cost per month) for the cheaper membership.

For Gym A, the rate of change of cost per month (k₁) is:
k₁ = y₁ / x₁ = 50 / 5 = 10

For Gym B, the rate of change of cost per month (k₂) is:
k₂ = y₂ / x₂ = 40 / 3 ≈ 13.33

Comparing the two rates of change, we can see that k₁ < k₂. Therefore, the value of k for the cheaper membership is 10.