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?(1 point)

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 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

For Gym A:

The cost is $50 for 5 months, so the equation is y = kx where k = 50/5 = 10.

For Gym B:
The cost is $40 for 3 months, so the equation is y = kx where k = 40/3 = 13.33 (rounded to 2 decimal places).

Since the goal is to find the cheaper membership, we need to find the smaller value of k.
Therefore, the value of k for the cheaper membership is 10.

Answer 2

To figure out which membership would be cheaper for a year, we need to calculate the cost per month for each membership.

For membership at Gym A:
Cost of membership = $50
Number of months = 5
Cost per month = $50/5 = $10

For membership at Gym B:
Cost of membership = $40
Number of months = 3
Cost per month = $40/3 ≈ $13.33

Now, let's write the equations in the form of y = kx:

For Gym A, y = 10x
For Gym B, y = 13.33x

Since we want to find the value of k for the cheaper membership, we compare the two equations:

10x < 13.33x

To find the value of k that makes the left side smaller than the right side, we need to find the value of x where the inequality holds true:

10 < 13.33

Since the inequality is true for all positive values of x, the value of k for the cheaper membership is 10.

Answer 3

To figure out which membership would be cheaper for a year, let's start by defining our variables:

Let y represent the cost of the membership.
Let x represent the number of months.
Let's write the equations for each gym membership:

For Gym A: y = kx
For Gym B: y = kx

Now, we know that a membership at Gym A costs $50 for 5 months, so we can plug in this information into the equation for Gym A:

50 = k(5)

Simplifying the equation, we get:

50 = 5k

Divide both sides of the equation by 5:

10 = k

So, the value of k for Gym A is 10.

Similarly, for Gym B, we know that the membership costs $40 for 3 months:

40 = k(3)

Simplifying the equation, we get:

40 = 3k

Divide both sides of the equation by 3:

k = 40/3 ≈ 13.33

Now, we can compare the values of k for both gym memberships. Since k = 10 for Gym A and k ≈ 13.33 for Gym B, we can conclude that Gym A has the cheaper membership for a year.