Let 100 g of the nugget contains x g gold. Then the amount of quartz will be (100 – x) .
Now, as the nugget is a mixture of solids, the volume of nugget may be assumed as the sum of volumes of gold and quartz present in it.
Vnugget = Vgold + Vquartz
100/6.4 = x/19.3 + (100-x)/2.6
Mass of gold present, x = 67.92 g