Question 1033173
Let {{{ x }}} = grams of the 45% gold coin needed
{{{ .45x }}} = grams of pure gold in {{{ x }}}
grams of 45% gold coin
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{{{ ( .45x + 11 ) / ( x + 11 ) = .71 }}}
{{{ .45x + 11 = .71*( x + 11 ) }}}
{{{ .45x + 11 = .71x + 7.81 }}}
{{{ .26x = 3.19 }}}
{{{ x = 12.27 }}}
12.27 grams of the 45% gold coin are needed
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check:
{{{ ( .45x + 11 ) / ( x + 11 ) = .71 }}}
{{{ ( .45*12.27 + 11 ) / ( 12.27 + 11 ) = .71 }}}
{{{ ( 5.522 + 11 ) / 23.27 = .71 }}}
{{{ 16.52 / 23.27 = .71 }}}
{{{ .7099 = .71 }}}
close enough