Question

I rent a gym for $150 for 30 students another time I rent the gym for $270 for 70 students I need to find a fixed rate

Answer 1

The fixed rate for the gym is $
`60`.

Explanation:

Given the price to rent a gym is $
`150` for
`30` students.

And another rent of the gym is $
`270` for
`70` students

Let
`x` be the number of student and
`y` be the amount of the gym.

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

`y=mx+b`

let us find the slope

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(270-150)/(70-30)\\\\m=(120)/(40)\\\\m=3`

Now, we will find y-intercept. Plug
`m=3` and coordinates of point
`(30,150)` in slope-intercept form of equation.

`(y-y_1)=m(x-x_1)\\y-150=3(x-30)\\y-150=3x-90\\y=3x-90+150\\y=3x+60`

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

Answer 2

Fixed rate is $60.

Explanation:

Let us consider per student charge be 'x'.

Let us consider fixed rate be 'b'

Given:

I rent a gym for $150 for 30 students.

So we can say that;

Total amount is equal to sum of number of students multiplied by per student charge and fixed rate.

framing in equation form we get;

`30x+b=150 \ \ \ \ equation \ 1`

Also Given:

another time I rent the gym for $270 for 70 students.

So we can say that;

Total amount is equal to sum of number of students multiplied by per student charge and fixed rate.

framing in equation form we get;

`70x+b=270 \ \ \ \ equation \ 2`

Now we will subtract equation 1 from equation 2 we get;

`70x+b-(30x+b)=270-150\\\\70x+b-30x-b=120\\\\40x=120`

Dividing both side by 40 we get;

`(40x)/(40)=(120)/(40)\\\\x=\$3`

Now we will substitute the value of x in equation 1 we get;

`30x+b=150\\\\30*3+b=150\\\\90+b=150\\\\b=150-90 =\$60`

So we can say that the equation can be written as;

`y =3x+60`

Hence we can say that fixed rate is $60 and per student charge is $3.