Question 529835
Let {{{x}}} = gallons of 15% antifreeze to be
removed and replaced with 80% antifreeze
In words:
( gallons of pure antifreeze at end)/( gallons of solution at end) = 70%
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{{{ .15*20 = 3 }}} gallons of pure antifreeze at start
{{{ 20 - x }}} gallons of solution left after removal of {{{x}}} gallons
{{{ .15*( 20 - x ) }}} = pure antifreeze left after removal of {{{x}}} gallons
{{{ .8x }}} = pure antifreeze in 80% solution added
The total gallons of solution has not changed
{{{ ( .8x + .15*( 20 - x ) ) / 20 = .7 }}}
{{{ .8x + 3 - .15x = 14 }}}
{{{ .65x = 11 }}}
{{{ x = 16.923 }}}
16.923 gallons must be removed and replace with 
16.923 gallons of 80% antifreeze
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check:
{{{ 20 - 16.923 = 3.077 }}} gallons of solution left after removal of {{{x}}} gallons
{{{ .15*( 20 - 16.923 ) = .4615 }}} = pure antifreeze left after removal of {{{x}}} gallons
{{{ .8*16.923 = 13.538 }}} = pure antifreeze in 80% solution added
{{{ ( .8x + .15*( 20 - x ) ) / 20 = .7 }}}
{{{ ( 13.538 + .4615 ) / 20 = .7 }}}
{{{ 13.9995 / 20 = .7 }}}
{{{ 13.9995 = 14 }}}
error due to rounding off- OK