A particular alloy is made of two metals. The density of one of the metals (call it metal A) is 3.0 g/cm3. The density of the other metal (call it metal B) is 5.0 g/cm3. If the density of the alloy is 4.0 g/cm3, what must be the percent composition of the alloy in terms of metal A and metal B?

50 % A and 50 % B

Explanation:

The densities of the metals for the alloy are additive according to the composition of the alloy, so we can establish the following relation:

Density of alloy = A x Density of A + B x density of B

where A and B are the percents divided by 100, and we do not need to concern with the units of densities since they appear in both sides of the equation.

Thus,

4 = 3 A + 5 B

But B = 1 - A:

4 = 3 A + 5 (1 - A) ⇒ 4 = 3A + 5 - 5A

4 = - 2A + 5 ⇒ - 2A = - 1 ⇒ A = 1/2 = 0.50

B = 1 - 0.50 = 0.50

Therefore the % composition is 50 % metal A + 50 % metal B