Question 498793
There can only be men, women, or children, so
Let {{{m}}} = number of men
Let {{{w}}} = number of women
given: 
(1) {{{ m + w + 1260 }}} = population
(2) {{{ m = .4*( m + w + 1260 ) }}}
(3) {{{ w = .39*( m + w + 1260 ) }}}
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(2) {{{ m = .4m + .4w + 504 }}}
(2) {{{ .6m - .4w = 504 }}}
(2) {{{ 60m - 40w = 50400 }}}
and
(1) {{{ w = .39m + .39w + 491.4 }}}
(1) {{{-.39m + .61w  =  491.4 }}}
(1) {{{ -39m + 61w = 49140 }}}
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Add the equations
(2) {{{ 60m - 40w = 50400 }}}
(1) {{{ -39m + 61w = 49140 }}}
{{{ 21m + 21w = 99540 }}}
{{{ 21*( m + w ) = 99540 }}}
{{{ m + w = 4740 }}}
and, since
{{{ m + w + 1260 }}} = population
{{{ 4740 + 1260 = 6000 }}} = population
Going back to (2)
(2) {{{ m = .4*( m + w + 1260 ) }}}
(2) {{{ m = .4*6000 }}}
(2) {{{ m = 2400 }}}
There are 2400 men
check the answer:
(3) {{{ w = .39*( m + w + 1260 ) }}}
(3) {{{ w = .39*6000 }}}
(3) {{{ w = 2340 }}}
and
(1) {{{ m + w + 1260 }}} = 6000
(1) {{{ 2400 + 2340 + 1260 = 6000 }}}
(1) {{{ 6000 = 6000 }}}
OK