Answer to Question #149374 in Algebra for bear

Question

a rectangular classroom seats 72 students. if 3 more seats were added to each row, the numbers of rows could be reduced by 2. find the original numbers of seats in each row.

Answer 1

The rectangular classroom seats 72 students

We mark

The number of rows in classroom - x;

The number of columns in classroom - y;

in the beginning x * y = 72

Then 3 more seats are added and the number of rows reduced by 2

x * y = 72 - first expression

(x + 3) * (y - 2) = second expression

xy - 2 * x + 3 * y - 6 = 72

3 * y - 2 * x = 6

3 * 72 / x - 2 * x = 6

216 - 2 * x² = 6 * x

x² + 3 * x - 108 = 0;

This is a quadratic equation

It is root 9

The answer the number of original seats in every row is that 9