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?
To find the value of k for the cheaper membership, let's set up the equations:
For Gym A, the equation would be:
y = 50x
For Gym B, the equation would be:
y = 40x
In order to determine which membership is cheaper for a year, we need to calculate the total cost for one year for each gym.
For Gym A, the cost for 12 months would be:
12 months * $50/month = $600
For Gym B, the cost for 12 months would be:
12 months * $40/month = $480
Now we can compare the two values:
For Gym A, the equation becomes:
y = 50x = $600
For Gym B, the equation becomes:
y = 40x = $480
From this comparison, we can conclude that the value of k for the cheaper membership is 40.
To determine the cheaper membership for a year, we need to compare the cost of 12 months of membership at both Gym A and Gym B.
For Gym A, the cost for 5 months is $50. We can set up the equation as follows:
y = kx
50 = k(5)
Simplifying, we have:
50 = 5k
Dividing both sides by 5, we find:
k = 10
So, the value of k for Gym A is 10.
For Gym B, the cost for 3 months is $40. Setting up the equation:
y = kx
40 = k(3)
Simplifying, we have:
40 = 3k
Dividing both sides by 3, we find:
k = 40/3
The value of k for Gym B is 40/3.
To determine which membership is cheaper for a year, we need to compare the cost of 12 months of membership for both gyms. We'll multiply the value of k by 12 for each gym:
For Gym A:
12 * k = 12 * 10 = 120
For Gym B:
12 * k = 12 * (40/3)
To compare the value of k for the cheaper membership, we need to find the smaller value between 120 and 12 * (40/3) = 160.
Since 120 is smaller than 160, the value of k for the cheaper membership is 10.
To compare the cost of the two memberships for a year, we need to calculate the cost per month for each membership.
For Gym A:
The cost is $50 for 5 months. Therefore, the cost per month at Gym A is $50 divided by 5 months, which is $10 per month.
For Gym B:
The cost is $40 for 3 months. Therefore, the cost per month at Gym B is $40 divided by 3 months, which is approximately $13.33 per month (rounded to two decimal places).
Now, let's write two equations in the form of y = kx, where y represents the cost and x represents the number of months.
For Gym A: y = 10x
For Gym B: y = 13.33x (rounded to two decimal places)
By comparing the equation coefficients, we can see that the value of k (the cost per month) for the cheaper membership is $10, which corresponds to Gym A.