Question 550577
Let {{{ x }}} = liters of 20% solution needed
given:
{{{ .5*40 = 20 }}} liters of alcohol in 50% solution
{{{ .2x }}} liters of alcohol in 20% solution
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{{{ ( 20 + .2x ) / ( 40 + x ) = .3 }}}
{{{ 20 + .2x = .3*( 40 + x ) }}}
{{{ 20 + .2x = 12 + .3x }}}
{{{ .1x = 20 - 12 }}}
{{{ .1x = 8 }}}
{{{ x = 80 }}}
80 liters of 20% solution are needed
check:
{{{ ( 20 + .2x ) / ( 40 + x ) = .3 }}}
{{{ ( 20 + .2*80 ) / ( 40 + 80 ) = .3 }}}
{{{ ( 20 + 16 ) / 120 = .3 }}}
{{{ 36 / 120 = .3 }}}
{{{ 36 = .3*120 }}}
{{{ 36 = 36 }}}
OK