There are 25 desks in a classroom. The number of rows is five less than twice the number of desks in each row. Find the number of rows and the number of desks in each row.

Let's say each row has x desks and there are y rows.

We then know that x*y = 25

We also know that x*2-5=y (number number of rows is five less than twice the number of desks in each row)

So we substitute: x * (x*2-5) = 25

putting numbers out of the brackets:

2x*x-5x=25

2x*x-5x-25=0

(2x+5) (x-5) = 0 (this bracketing is true: you can check it by expanding it:

2x*x-10x+5x-25

So that means that either x=-2.5which can't be : there can't be a fractional number of benches,

or x=5

so each row has 5 desks and there are 2*5-5 rows, or 5 rows.