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".]
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.