Question 1079457
Let {{{ a }}} = the number of men
Let {{{ b }}} = the nuber of women
Let {{{ c }}} = the number of children
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(1) {{{ a/b = 4/3 }}}
(2) {{{ b/c = 5/2 }}}
(3) {{{ a = c + 56 }}}
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Multiply (1) times (2)
{{{ ( a/b )*( b/c ) = (4/3)*(5/2) }}}
{{{ a/c = 10/3 }}}
{{{ c = (3/10)*a }}}
Plug this result into (3)
{{{ a = (3/10)*a + 56 }}}
{{{ (7/10)*a = 56 }}}
{{{ a = (10/7)*56 }}}
{{{ a = 80 }}}
and
(3) {{{ 80 = c + 56 }}}
(3) {{{ c = 24 }}}
and
(1) {{{ a/b = 4/3 }}}
(1) {{{ b = (3/4)*a }}}
(1) {{{ b = (3/4)*80 }}}
(1) {{{ b = 60 }}}
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{{{ a + b + c = 80 + 60 + 24  }}}
{{{ a + b + c = 164 }}}
There were 164 people at the game
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check:
(1) {{{ a/b = 4/3 }}}
(1) {{{ 80/60 = 4/3 }}}
(1) {{{ 4/3 = 4/3 }}}
OK
You can check (2) and (3)