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#
let the number of benches = #x#

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

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

Substituting equation 2 into equation 1

#3x + 3 = 4x - 12#

rearranging
#x = 15#

Substituting the value for x in equation 2
#y = 3* 15 + 3 = 48#