Specific gravity of gold:  19.259.


Specific gravity of quartz:  2.652.


Determine ounces of gold in an mass of 210 oz. of both, the specific gravity is  4.562.


Specific gravity is the weight of a volume of a substance divided by the weight of the same  volume of water. 

Water weighs 62.5 lbs. per cu. ft.     <<<---=== In my solution I do not need this info.
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First step is to find the fraction "x" of the gold in 210 oz. of mixture of the specific gravity 4.562.


For it, use the density equation

    x*19.259 + (1-x)*2.652 = 4.562.


    19.259x + 2.652 - 2.652x = 4.562  ====>  16.607x = 4.562 - 2.652 = 1.91  ====>  x =  = 0.115.


So, the mass fraction of the gold in the mixture is 0.115.



Next step determine the mass of the gold in the mass of 210 oz of the mixture:

    gold mass = 0.115*210 = 24.15 oz.