Answer: There are 48 students in the class.
Explanation:
Let the number of students = S
Let the number of benches = B
If 4 students sit on each bench, 3 benches are left vacant.
S = 4(B - 3)
S = 4·B - 12 } Equation 1
If 3 students sit on each bench, 3 students still standing.
S = 3·B + 3 } Equation 2
We can match the two equations because they both indicate the same number of students.
4B - 12 = 3·B + 3
on solving this
4·B - 3·B = 3 + 12
B = 15 → number of benches
That is the number of benches, therefore substituting the value for B in equation 1
S = 4·B - 12 Equation 1
S = 4·15 -12
S = 60 - 12 = 48 → number of students
Answer: There are 48 students in the class.
Verification
There are 48 students and 15 benches.
If 4 students sit on each bench, 3 benches are left vacant.
48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.
If 3 students sit on each bench, 3 students still standing.
15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.
Checked!!
