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?

Question

whats the answer

Answer 1

To determine the value of k for the cheaper membership, let's first establish the cost equation for each gym.

For Gym A:
Let y_1 be the cost of membership at Gym A and x_1 be the number of months.
We know that y_1 = 50 and x_1 = 5.
So the equation for Gym A can be written as y_1 = k_1 * x_1.

For Gym B:
Let y_2 be the cost of membership at Gym B and x_2 be the number of months.
We know that y_2 = 40 and x_2 = 3.
So the equation for Gym B can be written as y_2 = k_2 * x_2.

Now, let's compare the cost per year for each gym. Since a year consists of 12 months, we can calculate the cost equation for a year for both gyms.

For Gym A:
The cost for a year at Gym A would be y_1 * (12 / x_1) = (50) * (12 / 5) = 120.

For Gym B:
The cost for a year at Gym B would be y_2 * (12 / x_2) = (40) * (12 / 3) = 160.

Comparing the cost per year, we see that Gym A is cheaper with a cost of 120 compared to Gym B's cost of 160.

Since y_1 is the cost for Gym A's membership for 5 months and Gym A turns out to be cheaper for a year, we can conclude that k_1 is the value of the cheaper membership.
Thus, the value of k for the cheaper membership is k_1.