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