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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.

User Schoob
by
8.2k points

1 Answer

4 votes

Answer:

$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.

User PrashanD
by
8.3k points

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