Let the number of rows be = r
Let the number of seats per row be = s
we know that the number of seats is 126.
So, [tex]s\times r=126[/tex] ..... (1)
As given, there are five more seats per row than the number of rows, so we can say that:
[tex]s=r+5[/tex]
Putting this in equation (1)
[tex](r+5)*r=126[/tex]
[tex]r^{2}+5r=126[/tex]
[tex]r^{2}+5r-126=0[/tex]
[tex]r^{2}+14r-9r-126=0[/tex]
[tex](r+14)(r-9)=0[/tex]
r=-14 and r=9 (neglecting the negative value) we get r=9
And s=r+5
so, s =9+5=14
Hence, there are 5 rows and 14 seats per row.
