Question

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.

Answer 1

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.