SOLUTION: There are benches in a classroom. If 4 students sit on each bench, three benches are left vacant; and if 3 students sit on each bench three students are left standing. What is the

Question 1044116: There are benches in a classroom. If 4 students sit on each bench, three benches are left vacant; and if 3 students sit on each bench three students are left standing. What is the total number of students in the class.?
Found 2 solutions by solver91311, advanced_Learner:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the number of benches in the classroom. Then is the number of benches occupied by all of the students if they sit 4 to a bench. Hence, the number of students is . On the other hand, is the number of students that are seated if they sit 3 to a bench and there are 3 students left over. Hence, the number of students is also . Since the number of students doesn't change based on the way they are seated, we know that:

Solve for , then calculate either or

John

My calculator said it, I believe it, that settles it

Answer by advanced_Learner(501) (Show Source): You can put this solution on YOUR website!
If 4 students sit on each bench,
Number of benches sat on= x/4
Total number of benches available= (x/4)+3
If 3 students sit on each bench,
Number of benches needed= x/3
3 students are left standing
Thus, 1 bench is needed
Therefore, number of benches available= (x/3) -1
Thus,
(x/4)+3 = (x/3)-1
x/4 + 3= x/3 � 1
x/4 � x/3 = -1-3
3x/12 � 4x/12 = -4 (L.C.M)
-x/12 = -4
-x = -4*12
-x = -48
so, x=48
Number of students in the class = x = 48

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