Question 532769
It looks like 14 karat gold is {{{ 14/24 = .5833 }}}, or
58.33% pure gold
{{{ 18/24 = .75 }}}
18 karat gold is 75% pure gold
Let {{{ x }}} = ounces of 14 karat gold to be melted
{{{ .5833x }}} = ounces of pure gold in the 14 karat gold
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{{{ ( .5833x + 4 ) / ( x + 4 ) = .75 }}}
{{{ .5833x + 4 = .75x + 3 }}}
{{{ .75x - .5833x = 1 }}
{{{ .16667x = 1 }}}
{{{ x = 6 }}}
6 ounces of 14 karat gold should be melted
check:
{{{ ( .5833*6 + 4 ) / ( 6 + 4 ) = .75 }}} 
{{{ ( 3.5 + 4 ) / 10 = .75 }}}
{{{ 7.5/10 = .75 }}}
{{{ 7.5 = 7.5 }}}
OK