Question 1073712
THE FIFTH GRADE FACTORER says
{{{750=75*10=25*3*10=25*30}}} .
There were {{{25}}} children in each of {{{highlight(30)}}} rows.
 
THE ALGEBRA STUDENT says
Let {{{x}}} be the number of children in each row.
Then, {{{x+5}}} is the number of rows, and
{{{x(x+5)=750}}} is the number of children in school that day.
{{{x^2+5x=750}}} 
{{{x^2+5x-750=0}}}
Using the quadratic formula to solve that quadratic equation,
{{{x = (-5 +- sqrt( 5^2-4*1*(-750) ))/(2*1) }}}
{{{x = (-5 +- sqrt(25+3000 ))/2=(-5 +- sqrt(3025))/2=(-5 +- 55)/2}}}
The two solutions to that equation are
{{{x=(-5+55)/2=50/2=25}}} and
{{{x=(-5-55)/2=(-60)/2=-30}}} .
Since the number of children in each row cannot be a negative number.
{{{x=-30}}} is not a solution of the problem, so {{{x=25}}} ,
and the number of rows is {{{x+5=25+5=highlight(30)}}} .