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
𝑦
=
𝑘
𝑥
to try and figure out which membership would be cheaper for a year. What is the value of k
𝑘
for the cheaper membership?(1 point) .

Answer 1

To compare the memberships from Gym A and Gym B, we want to find the cost per month and see which one is cheaper over a year (12 months).

**Gym A:**
- Cost for 5 months: $50
- The cost per month (k) would be:
\[
k_A = \frac{50}{5} = 10
\]
- Cost for 12 months:
\[
y_A = k_A \times 12 = 10 \times 12 = 120
\]

**Gym B:**
- Cost for 3 months: $40
- The cost per month (k) would be:
\[
k_B = \frac{40}{3} \approx 13.33
\]
- Cost for 12 months:
\[
y_B = k_B \times 12 = \frac{40}{3} \times 12 = 160
\]

Now we compare the total costs for both gyms over 12 months:
- Total cost at Gym A for 12 months: $120
- Total cost at Gym B for 12 months: $160

Since $120 (Gym A) < $160 (Gym B), Gym A is the cheaper option.

The value of \( k \) for the cheaper membership (Gym A) is:

\[
k = 10
\]

Therefore, the value of \( k \) for the cheaper membership is \( \boxed{10} \).