Question

Rectangular classroom seats 72 students. If the seats were rearragned with 3 more seats rows in each row, the classroom would have 2 fewer rows.

Find the original number in each row?
[Hint: Let the original number of seats in a row be "X".]

Answer 1

Let the original number of seats in a row be x;
Let the number rows be y;

( x + 3) * (y - 2 )= 72 and x * y = 72 => 72 + 3 * y - 2 * x = 72 => 3 * y = 2 * x;
=> x is divisible by 3;

1. x = 3 => y = 72 / 3 => y = 24;
2. x = 6 => y = 72 / 6 => y = 12;
3. x = 9 => y = 72 / 9 => y = 8;
4. x = 12 => y = 72 / 12 =. y = 6;
5. x = 24 =. y = 72 / 24 => y = 3;
6. x = 36 => y = 72 / 36 => y = 2;
7. x = 72 => y = 72 / 72 => y = 1;

My analysis tell me that the right answer is 9 seats in a row and 8 rows;
The original number in each row is 9.