Question

In a class there are a certain number of seats. If each student occupies one seat, 9 students remain standing and if 2 students occupy one seat, 7 seats are left empty. Find the number of seats in the class.

Answer 1

Let the number of students be x and number of seats be y.
(i) When 2 students sit on one seat:
Number of seats occupied = y - 7
⇒ x = 2(y - 7)     .......(i)
(ii) When 1 student sit on one seats:
9 students are left standing
⇒ x - 9 = y
⇒ x = y + 9        .......(ii)
From (i) and (ii)
2(y - 7) = y + 9
2y - 14 = y + 9
y = 23
Therefore, Number of seats in the class = 23.