Question 687757
In {{{ 7 }}} liters of juice that contains 55% water, there is
{{{ .55*7 = 3.85 }}} liters of water
Let {{{ w }}} = liters of water to be added 
{{{ 7 - w }}} = liters of juice before adding water
{{{ .1*( 7 - w ) }}} = liters of water at the beginning

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( liters of water you end up with ) / ( liters of juice you end up with ) = .55
{{{ ( .1*( 7 - w ) + w ) / 7 = .55 }}}
{{{ ( .7 - .1*w + w ) / 7 = .55 }}}
{{{ ( .7 + .9w ) / 7 = .55 }}}
{{{ .7 + .9w = .55*7 }}}
{{{ .9w = 3.85 - .7 }}}
{{{ .9w = 3.15 }}}
{{{ w = 3.5 }}}
3.5 liters of water need to be added 
check:
{{{ .1*( 7 - w ) }}} = liters of water at the beginning
{{{ .1*( 7 - 3.5 )  = .35 }}} liters
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In {{{ 7 }}} liters of juice that contains 55% water, there is
{{{ .55*7 = 3.85 }}} liters of water
( liters of water you end up with ) - ( liters of water started with ) = ( liters of water to be added )
{{{ 3.85 - .35 = 3.5 }}} liters of water added