Question 697218
I will say that I have {{{ 5 }}} units of A
and {{{ 6 }}} units of B. It doesn't matter
what the unit is.
I mix them to get {{{ 11 }}} units of C.
given:
Let {{{ g }}} = units of gold
Let {{{ s }}} = units of silver
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For alloy A:
{{{ g/s = 1/2 }}}
{{{ 2g = s }}}
{{{ s = 2g }}}
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For alloy B:
{{{ g/s = 2/3 }}}
{{{ 3g = 2s }}}
{{{ s = (3/2)*g }}}
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Given:
{{{ C = A + B }}}
{{{ A/B = 5/6 }}}
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For alloy A:
{{{ s + g = 5 }}}
{{{ s = 2g }}}
{{{ 2g + g = 5 }}}
{{{ g = 5/3 }}}
{{{ s = 10/3 }}}
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For alloy B:
{{{ s + g = 6 }}}
{{{ (3/2)*g + g = 6 }}}
{{{ (5/2)*g = 6 }}}
{{{ g = 12/5 }}}
{{{ s = (3/2)*g }}}
{{{ s = 18/5 }}}
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Adding up the gold, I get
{{{ g = 5/3 + 12/5 }}}
{{{ g = 25/15 + 36/15 }}}
{{{ g = 61/15 }}}
Adding up the silver, I get
{{{ s = 10/3 + 18/5 }}}
{{{ s = 50/15 + 54/15 }}}
{{{ s = 104/15 }}}
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I need to find {{{ s / ( s + g ) }}}
for alloy C
{{{ s / ( s + g )  = ( 104/15 ) / ( 104/15  +  61/15 ) }}}
{{{ s / ( s + g ) = 104 / ( 104 + 61 ) }}}
{{{ s / ( s + g ) = 104 / 165 }}}
{{{ s / ( s + g ) = .6333 }}}
The percentage of silver is 63.333 %
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check answer:
{{{ .63333*11 = 6.93333 }}} units of silver
{{{ 11 - 6.93333 = 4.06666 }}} units of gold
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{{{ g = 61/15 }}}
{{{ 61/15 = 4.06666 }}}
and
{{{ s = 104/15 }}}
{{{ s = 6.93333 }}}
OK