Question 994496
Let {{{ x }}} = grams of pure gold needed
{{{ .4*( 100 - x ) }}} = grams of gold in 40% alloy
--------------------
{{{ ( x + .4*( 100 - x ) ) / 100 = .52 }}}
{{{ x + 40 - .4x = .52*100 }}}
{{{ .6x + 40 = 52 }}}
{{{ .6x = 12 }}}
{{{ x = 20 }}}
20 grams of pure gold are needed
-------------
check:
{{{ ( x + .4*( 100 - x ) ) / 100 = .52 }}}
{{{ ( 20 + .4*( 100 - 20 ) ) / 100 = .52 }}}
{{{ ( 20 + .4*80 ) / 100 = .52 }}}
{{{ 52 = .52*100 }}}
{{{ 52 = 52 }}}
OK