# Density and relative percentages

A bag contains a mixture of copper and lead BBs. The average density of the BBs is 9.80g/cm^3.

Assuming that the copper and lead are pure, how does one determine the relative amounts of each kind of BB?

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## migrated from chemistry.stackexchange.comSep 30 '12 at 11:53

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Hi Austin, this is not so much chemistry as it is maths… – F'x Sep 30 '12 at 11:53

Look up the densities of copper and lead from somewhere, and denote these by $\rho_c$ and $\rho_l$. Since we are interested in relative amount only, we can assume that the volume of BB's is altogether one unit, say $1 cm^3$, and split it into 2 parts: $x$ and $1-x$ (both in $cm^3$): $x$ is the volume of copper BB's, say.
So, considering the masses, denoting $\bar\rho$ the known average density: $$x\cdot\rho_c +(1-x)\cdot\rho_l = 1\cdot\bar\rho$$