A nugget of gold and quartz weighs 100g.  the densities of the gold, quartz, and the nugget are 19.3, 2.65, and 6.4g/cm^3, respectively.  determine the weight of the gold in the nugget.

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let x = mass of gold.  let y = mass of quartz x + y = 100    the sum of the masses is 100g (x / 19.3) + (y / 2.65) = (100 / 6.4)    This says the sum of the volumes equals the total volume. Use your favorite 2 equation, 2 unknown method to solve for x and y.  You could say x = 100 -y and substitute this into the second equation.  You get: x = 67.9 g of gold and y = 32.1 g of quartz