Respuesta :
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.
[tex]y=mx+b[/tex], where,
m = Slope of the line,
b = y-intercept or initial value.
Let us find slope of our line using slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Upon substituting coordinates of our points (30,150) and (70,270) in slope formula we will get,
[tex]m=\frac{270-150}{70-30}[/tex]
[tex]m=\frac{120}{40}[/tex]
[tex]m=3[/tex]
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.
[tex]150=3*30+b[/tex]
[tex]150=90+b[/tex]
[tex]150-90=90-90+b[/tex]
[tex]60=b[/tex]
So the equation [tex]y=3x+60[/tex] 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.
