## 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 densitythen a volumeof this metal has a mass

Suppose that metal 2 has a densitythen a volumeof this metal has a massThe two metals are mixed, so the total mass isand the total volume is

The density of the mixture will be and this density will be somewhere betweenanddepending on the ratio of metal 1 to metal 2 in the mixture.

Suppose the ratio isby mass then the mass of metal 1 in the mixture isand the mass of metal 2 is

Alsoand

so that

Then

Suppose that the two metals have densities ofandand are mixed in the mass ratio 3:5. Then

Suppose the ratio isby volume then the volume of metal 1 in the mixture isand the volume of metal 2 is

Alsoand

so that

Then

Suppose that the two same metals with densities ofandare mixed in the volume ratio 3:5 . Then