Combining Substances in a Certain Ratio to Give a Set Density

Substances are often combined to make new substances. Metal alloys are made by mixing metals together in certain proportions to give certain properties of strength, hardness, density or some other quality. If it is required that the density be a certain value then we can calculate the proportions in which the metals should be combined (this calculation applies to all mixing of substances, not just metals).

Suppose that metal 1 has a density then a volume of this metal has a mass Suppose that metal 2 has a density then a volume of this metal has a mass The two metals are mixed, so the total mass is and the total volume is The density of the mixture will be and this density will be somewhere between and depending on the ratio of metal 1 to metal 2 in the mixture.

Suppose the ratio is by mass then the mass of metal 1 in the mixture is and the mass of metal 2 is Also and so that Then Suppose that the two metals have densities of and and are mixed in the mass ratio 3:5. Then Suppose the ratio is by volume then the volume of metal 1 in the mixture is and the volume of metal 2 is Also and so that Then Suppose that the two same metals with densities of and are mixed in the volume ratio 3:5 . Then  