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

Answer:

Fixed rate is $60.

Step-by-step 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;

$\frac{40x}{40}=\frac{120}{40}\\\\x=\ 3$

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

$30x+b=150\\\\30\times3+b=150\\\\90+b=150\\\\b=150-90 =\ 60$

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.

Answer 2

Answer:

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

Step-by-step 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

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{270-150}{70-30}\\\\m=\frac{120}{40}\\\\m=3$

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$.