Question 749685
The key here is to realize that you start with
55 gallons and end up with 55 gallons
Let {{{ x }}} = gallons of solution to be drained 
and replaced with pure antifreeze
{{{ .55x }}} = gallons of antifreeze removed
{{{ .55*55 = 30.25 }}} gallons of antifreeze 
in original mixture
----------------------------
{{{ ( 30.25 - .55x + x ) / 55 = .7 }}}
{{{ ( 30.25 + .45x ) / 55 = .7 }}}
{{{ 30.25 + .45x = .7*55 }}}
{{{ 30.25 + .45x = 38.5 }}}
{{{ .45x = 8.25 }}}
{{{ x = 18.333 }}}
18.333 gallons of solution must be drained and
replaced with pure antifreeze
check:
{{{ ( 30.25 + .45x ) / 55 = .7 }}}
{{{ ( 30.25 + .45*18.333 ) / 55 = .7 }}}
{{{ 38,5 / 55 = .7 }}}
{{{ 38.5 = .7*55 }}}
{{{ 38.5 = 38.5 }}}
OK