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
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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):
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
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
