What is the initial fee? What is the rate of change?

Question

in order to use the school gym for practice the basketball team is charged a usage fee plus an hourly rate. To use the gym for 5 hours it would cost $170. Two hours of gym time would coat $95

Answer 1

Hi, let's see if we can establish a pattern for solving this type of problem.

We have two equations given in the problem. One for each gym practice situation. We know that the cost of the usage fee will be constant and the hourly rate is constant, but changes according to the amount of time spent in the gym.

For this problem, I created the two equations with the given information.

2X + B = 95

5X + B = 170

Isolate the B on both equations:

B= 95 - 2X

B = 170 - 5X

Since the value of B is the same for both equations, set them equal to each other and solve for X.

95- 2X = 170 - 5X

-75 = -3X

25 = X

Now substitute the value of X into one of the original equations to find the value for B.

2 (25) + B = 95

50 + B = 95

B = 45

The usage fee is $45 and the rate is $25 per hour.

Double check your work by substituting the rates into the equations and verifying they equal the stated amount.