Question

Question

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 point)

Answer 1

To compare the costs of the two gyms over a year, we first need to find the cost per month for each gym and then calculate the yearly cost.

1. Gym A:

   • Cost for 5 months: $50
   • Cost per month: \( \frac{50}{5} = 10 \)
   • Thus, the equation in the form \( y = kx \) is: \[ y = 10x \]
   • Here, \( k = 10 \).

2. Gym B:

   • Cost for 3 months: $40
   • Cost per month: \( \frac{40}{3} \approx 13.33 \)
   • Thus, the equation in the form \( y = kx \) is: \[ y \approx 13.33x \]
   • Here, \( k \approx 13.33 \).

To determine which gym is cheaper for a year (12 months):

• Yearly cost for Gym A: \[ Y_A = 10 \times 12 = 120 \]

• Yearly cost for Gym B: \[ Y_B \approx 13.33 \times 12 \approx 160 \]

Since Gym A costs $120 for the year and Gym B costs approximately $160 for the year, Gym A is the cheaper membership.

Thus, the value of \( k \) for the cheaper membership (Gym A) is: \[ k = 10 \]