Question 632802
seats = rows x columns
Let {{{ n }}} = number of seats in each row
given:
{{{ n }}} = number of rows - {{{ 12 }}}
Number of rows = {{{ n + 12 }}}
The number of columns is {{{ n }}}
{{{ n*( n + 12 ) = 2268 }}}
{{{ n^2 + 12n = 2268 }}}
Complete the square
{{{ n^2 + 12n + (12/2)^2 = 2268 + (12/2)^2 }}}
{{{ n^2 + 12n + 36 = 2268 + 36 }}}
{{{ ( n + 6 )^2 = 2304 }}}
{{{ ( n + 6 )^2 = 48^2 }}}
{{{ n + 6 = 48 }}}
{{{ n = 42 }}}
There are 42 seats in each row
check:
Number of rows = {{{ n + 12 }}}
{{{ n + 12 = 54 }}}
{{{ 42*54 = 2268 }}}
{{{ 2268 = 2268 }}}
OK