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

Question

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 determine the monthly cost of each gym, we first need to express the total cost of each membership for one year (12 months) in terms of the number of months purchased.

For Gym A:

• The cost for 5 months is $50.

• The cost per month can be calculated as:

  \[ \text{Cost per month} = \frac{50}{5} = 10 \text{ dollars/month} \]

• For 12 months, the total cost would be:

  \[ \text{Total cost for Gym A} = 10 \times 12 = 120 \text{ dollars} \]

For Gym B:

• The cost for 3 months is $40.

• The cost per month can be calculated as:

  \[ \text{Cost per month} = \frac{40}{3} \approx 13.33 \text{ dollars/month} \]

• For 12 months, the total cost would be:

  \[ \text{Total cost for Gym B} = 13.33 \times 12 \approx 160 \text{ dollars} \]

Now let's summarize the findings:

• Total cost for Gym A for 12 months is $120.
• Total cost for Gym B for 12 months is approximately $160.

Conclusion: Gym A is the cheaper membership for a year.

To write the equations in the form of \( y = kx \), we can recognize that \( k \) represents the monthly cost.

• For Gym A, \( k = 10 \).
• For Gym B, \( k \approx 13.33 \).

Thus, the value of \( k \) for the cheaper membership (Gym A) is \( 10 \).