A membership at gym a cost $50 for 5 months a membership at Jim B down the street cost $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

Answer 1

Let's denote the cost of Gym A and Gym B as follows:

1. Gym A:

   • Cost: $50 for 5 months
   • Cost per month \( K_A = \frac{50}{5} = 10 \)
   • The equation will be in the form \( Y = K_A X \), where \( Y \) is the total cost and \( X \) is the number of months.
   • So, \( Y = 10X \).

2. Gym B:

   • Cost: $40 for 3 months
   • Cost per month \( K_B = \frac{40}{3} \approx 13.33 \)
   • The equation will be \( Y = K_B X \), where \( K_B \approx 13.33 \).
   • So, \( Y = \frac{40}{3} X \) or approximately \( Y \approx 13.33X \).

Now, let's calculate the total cost for each gym for a year (12 months):

• Cost for Gym A for 12 months: \[ Y_A = 10 \times 12 = 120 \text{ dollars} \]

• Cost for Gym B for 12 months: \[ Y_B = \frac{40}{3} \times 12 = \frac{480}{3} = 160 \text{ dollars} \]

Now comparing the costs for a year:

• Cost of Gym A for 12 months: $120
• Cost of Gym B for 12 months: $160

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

Conclusion

The value of \( K \) for the cheaper membership (Gym A) is $10.