In a class, if 4 students sit on each bench, then 3 benches remain empty. But if 3 students sit on each bench, then 6 students have to stand. What…

Let the number of benches be \(b\).

4 per bench with 3 benches empty: students = \(4(b - 3)\). 3 per bench with 6 standing: students = \(3b + 6\).

\(4(b - 3) = 3b + 6 \Rightarrow 4b - 12 = 3b + 6 \Rightarrow b = 18\)

Students = 3 × 18 + 6 = 60. Check: 4 × (18 − 3) = 60.

— rhs