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

To compare the cost of the memberships for a year, we need to determine the cost per month for each membership.

For Gym A:
The cost for 5 months is $50.
So, the cost per month (y) at Gym A can be represented by the equation y = kx, where x is the number of months:
50 = 5k

And for Gym B:
The cost for 3 months is $40.
So, the cost per month (y) at Gym B can be represented by the equation y = kx, where x is the number of months:
40 = 3k

To find the value of k for the cheaper membership, we need to compare the two equations. Since we want to find the cheaper membership, we can compare the values of k for Gym A and Gym B.

From the equation 50 = 5k, we can solve for k by dividing both sides by 5:
50/5 = 5k/5
10 = k

From the equation 40 = 3k, we can solve for k by dividing both sides by 3:
40/3 = 3k/3
40/3 ≈ 13.333... = k

Comparing the values of k for Gym A and Gym B, we can see that k = 10 is smaller than k ≈ 13.333..., making the cost per month at Gym A (using the equation y = kx) cheaper than at Gym B. Thus, the value of k for the cheaper membership is 10.

Answer 2

Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.(

Answer 3

To represent the motion of the faster car, we need to find the equation for Road 2, where the car can go 90 miles in 4 hours.

We can express this relationship using the equation y = kx, where y is the distance in miles and x is the time in hours.

Since on Road 2, the car can go 90 miles in 4 hours, we can substitute y = 90 and x = 4 into the equation.

90 = k * 4

To find the value of k, we can solve for k by dividing both sides by 4:

90/4 = k * 4/4
22.5 = k

Therefore, the equation that represents the motion of the faster car is y = 22.5x.