Question 713985
Let {{{ x }}} = ounces of 30% solution needed
{{{ .3x }}} = ounces of alcohol in 30% solution
{{{ .8*50 = 40 }}} ounces of alcohol in 80% solution
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{{{ ( .3x + 40 ) / ( x + 50 ) = .6 }}}
{{{ .3x + 40 = .6*( x + 50 ) }}}
{{{ .3x + 40 = .6x + 30 }}}
{{{ .3x = 40 - 30 }}}
{{{ .3x = 10 }}}
{{{ x = 33.333 }}}
The pharmacist needs 33 1/3 ounces of 30% solution
check:
{{{ ( .3x + 40 ) / ( x + 50 ) = .6 }}}
{{{ ( .3*33.333 + 40 ) / ( 33.333 + 50 ) = .6 }}}
{{{ ( 10 + 40) / 83.333 = .6 }}}
{{{ 50 = .6*83.333 }}}
{{{ 50 = 50 }}}
OK