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.
(y= mx+b)

Answer 1

Answer: y = 3x + 60

Step-by-step explanation:

Set up two equations and solve the system:

 270 = 70x + b

- (150 = 30x + b)

  120 = 40x

    3   =  x

Input "x" into one of the equations and solve for "b":

150 = 30x + b

150 = 30(3) + b

150 = 90 + b

60 = b

Equation: y = 3x + 60

This means that there is a flat fee of $60 plus a rate of $3 per student

Answer 2

The fixed rate of gym fee of $60 plus a rate of $3 per student.

The fixed-rate is;

$\rm y=3x+60$

Given

I rent a gym for $150.00 for 30 students.

Another time I rent the gym for $270.00 for 70 students.

Linear function;

A linear function is a function that forms a straight line in a graph.

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

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

The equation representing a fixed rate is;

$\rm y = mx+b$

I rent a gym for $150.00 for 30 students.

$\rm 150 = 30x + b$

Another time I rent the gym for $270.00 for 70 students.

$\rm 270 = 70x + b$

Subtracting both the equations;

$\rm 150-270=30x+b-70x-b\\\\-120=-40x\\\\120=4x\\\\x=\dfrac{120}{4}\\\\x=3$

Substitute the value of x in equation 1

$\rm 150 = 30x + b\\\\150=30(3)+b\\\\150=90+b\\\\b=150-90\\\\b=60$

Therefore,

The fixed-rate is;

$\rm y=mx+b\\\\y=3x+60$

Hence, the fixed rate of gym fee of $60 plus a rate of $3 per student.'

To know more about linear function click the link given below.

https://brainly.com/question/371915