A membership at Gym A cost $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?
Let's assume that x represents the number of months and y represents the cost of the membership.
For Gym A:
The membership at Gym A costs $50 for 5 months.
Therefore, the equation for Gym A is y = 50/5 * x, which simplifies to y = 10x.
For Gym B:
The membership at Gym B costs $40 for 3 months.
Therefore, the equation for Gym B is y = 40/3 * x, which simplifies to y = (40/3)x.
To determine which membership is cheaper for a year (12 months), we can compare the costs for x = 12.
For Gym A:
y = 10x
y = 10 * 12
y = 120
For Gym B:
y = (40/3)x
y = (40/3) * 12
y = 160
Comparing the costs, we can see that Gym A is cheaper for a year, with a cost of $120.
The value of k for the cheaper membership (Gym A) is therefore 10.
To determine the cheaper membership for a year, we need to compare the costs of the two gyms over a 12-month period. Let's set up the equations:
For Gym A, the cost, y, is a function of the number of months, x, using the equation y = kx. We know that the cost for 5 months is $50, so we have the equation 50 = k(5).
For Gym B, the cost, y, is also a function of the number of months, x, with the equation y = kx. The cost for 3 months at Gym B is $40, so we can write the equation 40 = k(3).
To find the value of k for the cheaper membership, we need to compare the rates of change, that is, the values of k.
For Gym A: 50 = k(5)
Divide both sides by 5: 10 = k
For Gym B: 40 = k(3)
Divide both sides by 3: 13.33 = k (approximated)
Comparing the two values of k, we can see that k = 10 for Gym A is cheaper than k = 13.33 for Gym B. Therefore, the value of k for the cheaper membership is 10.
To determine the value of k for the cheaper membership, let's set up the equations for the cost of each gym membership.
Let's assume y represents the total cost and x represents the number of months.
For Gym A, the equation is y = kx. Given that a membership at Gym A costs $50 for 5 months, we can substitute these values into the equation: 50 = 5k.
For Gym B, the equation is y = kx. Given that a membership at Gym B costs $40 for 3 months, we can substitute these values into the equation: 40 = 3k.
Now we can solve each equation for k:
For Gym A:
50 = 5k
Divide both sides by 5:
10 = k
For Gym B:
40 = 3k
Divide both sides by 3:
k = 40/3
k ≈ 13.33
Comparing the two values, we can see that k = 10 for Gym A is less than k ≈ 13.33 for Gym B. Therefore, the value of k for the cheaper membership is 10, corresponding to Gym A.