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?

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?

Answer 1

Let's assign y as the cost and x as the number of months for each gym membership.

For Gym A:
y = kx

Given that the cost for 5 months at Gym A is $50, we can solve for k:
50 = k * 5

Dividing both sides of the equation by 5, we get:
10 = k

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

For Gym B:
y = kx

Given that the cost for 3 months at Gym B is $40, we can solve for k:
40 = k * 3

Dividing both sides of the equation by 3, we get:
k = 40/3

The value of k for Gym B is approximately 13.33 (rounded to two decimal places).

To determine which membership would be cheaper for a year, we need to compare the cost for a 12-month period.

For Gym A:
Cost for 12 months = k * 12
Cost for 12 months = 10 * 12 = $120

For Gym B:
Cost for 12 months = k * 12
Cost for 12 months = 13.33 * 12 = $160

Comparing the costs, we can see that the membership at Gym A would be cheaper for a year, with a value of k equal to 10.

Answer 2

Let's denote the cost of a membership at Gym A as y_A and the number of months as x_A. Similarly, let's denote the cost of a membership at Gym B as y_B and the number of months as x_B.

For Gym A, since the cost is $50 for 5 months, we have:

y_A = k_A*x_A
50 = k_A*5

For Gym B, since the cost is $40 for 3 months, we have:

y_B = k_B*x_B
40 = k_B*3

To figure out which membership would be cheaper for a year, we can compare the total cost for 12 months. Therefore, we need to solve for y_A and y_B over 12 months.

For Gym A, over 12 months, we have:
12*y_A = k_A*12*x_A
12*y_A = k_A*12*5
12*y_A = 60*k_A
y_A = 5*k_A

For Gym B, over 12 months, we have:
12*y_B = k_B*12*x_B
12*y_B = k_B*12*3
12*y_B = 36*k_B
y_B = 3*k_B

To determine which membership is cheaper, we need to find the value of k that makes y_A or y_B smaller.

Comparing y_A = 5*k_A and y_B = 3*k_B, we can see that for the same value of k, y_B will always be smaller since 3 is smaller than 5.

Therefore, the value of k for the cheaper membership is k_B.

Answer 3

To simplify the answer, we can say that the value of k for the cheaper membership is k = k_B.

Answer 4

You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?

Answer 5

To calculate the average rate of speed, we can use the equation:

Rate of speed = Distance / Time

For the first route, where it takes 8 hours to drive 400 miles, the rate of speed (RS_1) is:

RS_1 = 400 / 8
RS_1 = 50 miles per hour

For the second route, where it takes 7 hours to drive 420 miles, the rate of speed (RS_2) is:

RS_2 = 420 / 7
RS_2 = 60 miles per hour

To determine how much higher your average speed would be on the faster route, we compare the two rates of speed:

Difference = RS_2 - RS_1
Difference = 60 - 50
Difference = 10 miles per hour

Therefore, your average speed on the faster route would be 10 miles per hour higher than the slower route.

Answer 6

To compare which membership would be cheaper for a year, we need to find the cost per month for each membership, and then calculate the total cost for a year.

Let's start by writing the equation for the cost of the membership at Gym A. We know that the membership costs $50 for 5 months. Let's assign y as the cost and x as the number of months:

y = kx

For Gym A, we have:

50 = k(5)

Next, let's write the equation for the cost of the membership at Gym B. We know that the membership costs $40 for 3 months. Using the same variables, we get:

y = kx

For Gym B, we have:

40 = k(3)

Now, let's solve these equations to find the value of k for each gym:

For Gym A:

50 = 5k
k = 50/5
k = 10

For Gym B:

40 = 3k
k = 40/3
k ≈ 13.33 (rounded to two decimal places)

To determine the cheaper membership, we need to compare the cost per month. Gym A has a cost per month of k = $10, while Gym B has a cost per month of k ≈ $13.33.

Therefore, the value of k for the cheaper membership is $10.