Question

there are some benches in the classroom. if 4 students sit on each bench, 3 benches are left vacant but if 3 students sit on each bench, 3 students are left standing. what is the total no. of students in the class

Answer 1

let the no of benches =X
so students will be
4(X-3)
and also in the second equation
the no of students= 3X+3
then
4X-12=3X +3
on solving this
X=15
no. of benches =15
no. of students=45+3=48

Answer 2

The total no. of students in the class is 48.

Step-by-step explanation:

We are given that there are some benches in the classroom. If 4 students sit on each bench, 3 benches are left vacant but if 3 students sit on each bench, 3 students are left standing.

Let the total number of benches be 'x' and the total number of students be 'y'.

So, according to the question;

• The first condition states that if 4 students sit on each bench, 3 benches are left vacant, that means;

                                  $y=4x - (4 \times 3)$

                                  $y=4x - 12$   ---------------- [Equation 1]

• The second condition states that if 3 students sit on each bench, 3 students are left standing, that means;

                                  $y=3x+3$   ------------------- [Equation 2]

From equation 1 and 2, we get;

                      $4x-12 = 3x+3$

                      $4x-3x =3+12$

                       $x=15$

Now, substituting the value of x in equation 1 get;

                      y = 4x - 12

                      y = $(4 \times 15) -12$                

                      y = 60 - 12 = 48

Hence, the total no. of students in the class is 48.