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?
A membership at Gym A costs $50 for 5 months, so it costs $50/5 = $<<50/5=10>>10 a month. This means the value of k for Gym A is 10.
On the other hand, a membership at Gym B costs $40 for 3 months. This means it costs $40/3 = $<<40/3=13.333333333333334>>13.33 (rounded to the nearest cent) a month.
Therefore, the cheaper membership is the one with a lower value of k. We have to find the lower value between 10 and 13.33. The value of k for the cheaper membership is $<<10=10>>10 a month. Answer: \boxed{10}.
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.
On Road 1, the car can go 60 miles in 2 hours, so it goes at a speed of 60/2 = 30 miles per hour. This means the equation for Road 1 is y = 30x.
On Road 2, the car can go 90 miles in 4 hours, so it goes at a speed of 90/4 = 22.5 miles per hour. This means the equation for Road 2 is y = 22.5x.
The faster car is the one with a higher value of k, or the car on Road 1. The equation representing its motion is y = 30x.
So, the equation representing the motion of the faster car is \boxed{y = 30x}.
Let's denote:
- x as the number of months
- y as the cost of the membership
For Gym A:
y = kx
Since the cost of Gym A is $50 for 5 months, we can substitute the values:
50 = k * 5
For Gym B:
y = kx
Since the cost of Gym B is $40 for 3 months, we can substitute the values:
40 = k * 3
To find the value of k for the cheaper membership, we need to solve both equations. Let's solve them one by one:
For Gym A:
50 = k * 5
Dividing both sides by 5:
10 = k
For Gym B:
40 = k * 3
Dividing both sides by 3:
k ≈ 13.33
Comparing the two values of k, we see that the value of k for the cheaper membership is 10.
To determine the cheaper membership for a year, we need to compare the costs of Gym A and Gym B over a 12-month period.
Let's write the equation for Gym A's membership cost: y = kx, where y represents the cost and x represents the number of months. According to the given information, a Gym A membership costs $50 for 5 months. Therefore, we can substitute these values into the equation:
50 = 5k
Now, let's write the equation for Gym B's membership cost. Again, y = kx, where y represents the cost and x represents the number of months. We know that a Gym B membership costs $40 for 3 months. So, the equation becomes:
40 = 3k
To find the value of k, we can solve these equations for k.
For Gym A:
50 = 5k
Divide both sides by 5:
10 = k
For Gym B:
40 = 3k
Divide both sides by 3:
13.333 = k
Comparing the values of k for Gym A and Gym B, we can see that k = 10 for Gym A and k = 13.333 for Gym B. Since we need to find the value of k for the cheaper membership, we can conclude that the value of k for the cheaper membership is 10, corresponding to Gym A.