Numerical answer
In a classroom, if 3 students sit on each bench, 5 students are left without a seat. If 4 students sit on each bench, 3 benches remain completely empty and every other bench is full. How many students are there in the class?
Show answer and solution
Answer: 56
Let the number of benches be b.
Case 1: students = 3b + 5.
Case 2: only (b − 3) benches are used, each with 4 students: students = 4(b − 3).
3b + 5 = 4b − 12 → b = 17.
Students = 3 × 17 + 5 = 56. (Check: 4 × 14 = 56 ✓.)
Case 1: students = 3b + 5.
Case 2: only (b − 3) benches are used, each with 4 students: students = 4(b − 3).
3b + 5 = 4b − 12 → b = 17.
Students = 3 × 17 + 5 = 56. (Check: 4 × 14 = 56 ✓.)
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