Question 962125
Let {{{ a }}} = number of men on N.C.
Let {{{ b }}} = number of men on S.C.
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(1) {{{ a + b = 150 }}}
(2) {{{ .05a + .8b = .5*150 }}}
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(2) {{{ .05a + .8b = 75 }}}
(2) {{{ 5a + 80b = 7500 }}}
Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5a + 80b = 7500 }}}
(1) {{{ -5a - 5b = -750 }}}
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{{{ 75b = 6750 }}}
{{{ b = 90 }}}
and
(1) {{{ a + b = 150 }}}
(1) {{{ a = 150 - 90 }}}
(1) {{{ a = 60 }}}
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There were 60 men on N.C.
There were 90 men on S.C.
check:
(2) {{{ .05a + .8b = 75 }}}
(2) {{{ .05*60 + .8*90 = 75 }}} 
(2) {{{ 3 + 72 = 75 }}}
(2) {{{ 75 = 75 }}}
OK