Question 996547
Let {{{ x }}} = liters of 52% solution needed
{{{ .24*30 = 7.2 }}} liters of 24% solution
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 {{{ ( .52x + 7.2 ) / ( x + 30 ) = .4 }}}
{{{ .52x + 7.2 = .4*( x + 30 ) }}}
{{{ .52x + 7.2 = .4x + 12 }}}
{{{ .12x = 4.8 }}}
{{{ x = 40 }}}
40 liters of 52% solution are needed
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check:
 {{{ ( .52x + 7.2 ) / ( x + 30 ) = .4 }}}
 {{{ ( .52*40 + 7.2 ) / ( 40 + 30 ) = .4 }}}
{{{ ( 20.8 + 7.2 ) / 70 = .4 }}}
{{{ 28/70 = .4 }}}
{{{ 28 = .4*70 }}}
{{{ 28 = 28 }}}
OK