Question 997875
Let {{{ x }}} = liters of 50% alcohol needed
{{{ .5x }}} = liters of alcohol in 50% solution
{{{ .8*90 = 72 }}} liters of alcohol in 80% solution
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{{{ ( .5x + 72 ) / ( x + 90 ) = .7 }}}
{{{ .5x + 72 = .7*( x + 90 ) }}}
{{{ .5x + 72 = .7x + 63 }}}
{{{ .2x = 9 }}}
{{{ x = 45 }}}
45 liters of 50% alcohol are needed
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check:
{{{ ( .5x + 72 ) / ( x + 90 ) = .7 }}}
{{{ ( .5*45 + 72 ) / ( 45 + 90 ) = .7 }}}
{{{ ( 22.5 + 72 ) / 135 = .7 }}}
{{{ 94.5 = .7*135 }}}
{{{ 94.5 = 94.5 }}}
OK