[Problems on Mixtures and Concentrations]

An alloy of gold and silver weighing 13 kg 850 g, when fully submerged in water, displaced 900 g of water. Determine the amount of gold and silver in this alloy, given that the density of gold is 19.3 kg/dm${}^{3}$, and that of silver is 10.5 kg/dm${}^{3}$.
From the condition, it is clear that the volume of the alloy is 0.9 dm ${}^{3}$. If it were made of pure gold, its mass would be $0.9 \cdot 19.3=17.37$ kg. The extra

$17.37-13.85$ = 3.52 kg resulted from replacing some cubic decimeters of silver with gold. Each cubic decimeter of gold is

$19.3-10.5=8.8$ kg heavier than the same volume of silver. Therefore, the amount of silver was $3.52: 8.8=0.4$ dm ${}^{3}$. The mass of silver is $0.4 \cdot 10.5=4.2$ kg, and the mass of gold is

$13.85-4.2=9.65$ kg.

## Answer

Gold - 9.65 kg, silver - 4.2 kg.

## Problem