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 members?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare the cost of the memberships for one year, we need to convert the given durations to 12 months.

For Gym A: $50 for 5 months, so $50 * (12 months / 5 months) = $120 per year.
For Gym B: $40 for 3 months, so $40 * (12 months / 3 months) = $160 per year.

Let's represent the cost of the membership for Gym A as y = kx, where y is the total cost and x is the number of months. For Gym A, we have y = kA, where A represents the number of months.

Similarly, for Gym B, we have y = kB, where B represents the number of months.

From the given information, we know that kA = 120 and kB = 160.

To find the value of k for the cheaper membership, we need to compare the values of kA and kB.

120 is less than 160, so kA is the smaller value. Therefore, the value of k for the cheaper membership is 120.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the value of k for the cheaper membership, we can set up two equations:

For Gym A: y = 50x/5

For Gym B: y = 40x/3

Here, y represents the cost of the membership, and x represents the number of months.

To compare the cost for a year, we need to calculate the cost for 12 months.

For Gym A: y = 50(12)/5 = 600/5 = 120

For Gym B: y = 40(12)/3 = 480/3 = 160

From the calculations, we can see that the cost for a year at Gym A is $120, while the cost for a year at Gym B is $160.

Hence, the value of k for the cheaper membership is 120.

Answer 3

[AI-generated answer — Explain Bot]

To determine which membership is cheaper for a year, we need to compare the cost of both gyms over the span of one year.

Let's first determine the cost of 1 year at Gym A. We know that a membership at Gym A costs $50 for 5 months, so the cost per month (k) can be calculated as $50 / 5 = $10 per month. Therefore, the equation for Gym A can be written as y = 10x, where y represents the cost and x represents the number of months.

Next, we need to determine the cost of 1 year at Gym B. A membership at Gym B costs $40 for 3 months, so the cost per month (k) is calculated as $40 / 3 = $13.33 (rounded to two decimal places) per month. Thus, the equation for Gym B can be written as y = 13.33x.

To compare the cost of both memberships over one year, we need to find the value of y when x = 12 (representing 12 months in a year) for both equations.

For Gym A, substituting x = 12 into the equation y = 10x gives:
y = 10 * 12 = $120

For Gym B, substituting x = 12 into the equation y = 13.33x gives:
y = 13.33 * 12 = $159.96 (rounded to two decimal places)

Comparing the values, we see that a membership at Gym A costs $120 for a year, while a membership at Gym B costs $159.96 for a year. Therefore, the value of k for the cheaper membership is $10, which corresponds to Gym A.