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 ?

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Answer 1 · 2017-01-23T07:43:07

The number of students is 48

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

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

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

Substituting equation 2 into equation 1

$3 x + 3 = 4 x - 12$ $3x + 3 = 4x - 12$

rearranging
$x = 15$ $x = 15$

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