Question 1152433
Let {{{ n }}} = original number going on trip
{{{ n + 4 }}} = number with 4 more girls
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{{{ 280 / ( n + 4 ) = 280 / n - 8 }}}
multiply both sides by {{{ n*( n + 4 ) }}}
{{{ 280n = 280*( n + 4 ) - 8*n*( n + 4 ) }}}
{{{ 280n = 280n + 1120 - 8n^2 - 32n }}}
{{{ 8n^2 + 32n = 1120 }}}
{{{ n^2 + 4n - 140 = 0 }}}
{{{ ( n + 14 )*( n - 10 ) = 0 }}} ( by looking at it )
{{{ n = 10 }}} ( can't use the negative result )
and
{{{ n + 4 = 14 }}}
14 girls went on the trip
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check:
{{{ 280 / ( n + 4 ) = 280 / n - 8 }}}
{{{ 280 / ( 10 + 4 ) = 280 / 10 - 8 }}}
{{{ 280 / 14 = 28 - 8 }}}
{{{ 20 = 20 }}}
OK