Question 35460
With a little more thought, someone will probably come up with a cleaner and easier way to do this, but this is what I got for now.  It's a neat problem.  Nice one!!


Let x = total number of people in the stadium
{{{x/9}}} = number of men


Therefore the other {{{8x/9}}} = number of women and children


{{{(3/8)*((8x)/9)}}} = number of women
{{{x/3 }}} = number of women


Number of children = Number of Women + 400
Number of children =  {{{(x/3) + 400}}}
Women and Children= {{{(8x)/9 = (x/3)  + (x/3) + 400}}}

Women and Children= {{{(8x)/9 = (2x/3)  + 400}}}

Women and Children= {{{(8x)/9 = (6x/9) + 400}}}

Women and Children= {{{(2x)/9 =  400}}}


Multiply both sides by {{{9/2}}}

{{{(2x)/9 *(9/2) =  400*(9/2) }}}

{{{x = 1800 }}}


Check:  

Men = {{{1800/9 = 200}}}
Women = {{{ 1800/3 = 600}}}
Children = Women + 400 = {{{600+400 = 1000}}}
Total = 1800  so it checks!!


R^2 at SCC