Question 941069
{{{ .2*1 = .2 }}} gallons of lemon juice in 20% mix
Let {{{ x }}} = gallons of 70% mix to be added
{{{ .7x }}} = gallons of lemon juice in 70% mix
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{{{ ( .7x + .2 ) / ( x + 1 ) = .4 }}}
{{{ .7x + .2 = .4*( x + 1 ) }}}
{{{ .7x + .2 = .4x + .4 }}}
{{{ .3x = .2 }}}
{{{ x = 2/3 }}}
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The final mixture is 1 and 2/3 gallons 
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check:
{{{ ( .7*(2/3) + .2 ) / ( 2/3 + 1 ) = .4 }}}
{{{ ( ( 7/10 )*( 2/3 ) + 2/10 ) / ( 5/3 )  = 4/10 }}}
{{{ 7/15 + 2/10 = 10/15 }}}
{{{ 14/30 + 6/30 = 20/30 }}}
{{{ 20/30 = 20/30 }}}
OK