Question

I rent a gym for $150.00 for 30 students. Another time I rent the gym for

@270.00 for 70 students. I need to find a fixed rate.

Answer 1

$60.

Explanation:

Let x be the number of students and y be the total cost of renting the gym.

We are told that we rent a gym for $150.00 for 30 students. Another time we rent the gym for $270.00 for 70 students.

To find the fixed rate let us write the equation of line representing the total cost of renting gym for x students.

We will write equation of the line representing total cost in slope-intercept form of equation.

`y=mx+b`, where,

m = Slope of the line,

b = y-intercept or initial value.

Let us find slope of our line using slope formula.

`m=(y_2-y_1)/(x_2-x_1)`

Upon substituting coordinates of our points (30,150) and (70,270) in slope formula we will get,

`m=(270-150)/(70-30)`

`m=(120)/(40)`

`m=3`

Therefore, the slope of our line is 3, which represents cost of using gym per student.

Let us substitute m=3 and coordinates of point (30,150) in slope-intercept form of equation.

`150=3*30+b`

`150=90+b`

`150-90=90-90+b`

`60=b`

So the equation
`y=3x+60` represents the total cost of renting gym for x students.

As total cost of renting gym includes charges per student plus fixed rate. The cost of using gym per student is $3.

Since, y-intercept represents the initial value. Therefore, the fixed rate for the gym is $60.