# There are students and benches in a classroom . If 4 students sit in each bench, 3 benches are left vacant.But if 3 students sit in a bench, 3 students are left standing.What are the total no. of students ?

Jan 23, 2017

The number of students is 48

#### Explanation:

Let the number of students = $y$
let the number of benches = $x$

from the first statement
$y = 4 x - 12$ (three empty benches * 4 students)

from the second statement
$y = 3 x + 3$

Substituting equation 2 into equation 1

$3 x + 3 = 4 x - 12$

rearranging
$x = 15$

Substituting the value for x in equation 2
$y = 3 \cdot 15 + 3 = 48$