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

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}.

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

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}.