Question

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

Answer 1

Answer:

$60.

Step-by-step 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.

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{270-150}{70-30}$

$m=\frac{120}{40}$

$m=3$

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.