Question $8.$ For a solid consisting of two elements $($designated as $1$ and $2),$ sometimes it is

desirable to determine the number of atoms per cubic centimeter of one element in a solid solution,

$N_1,$ given the concentration of that element specified in weight percent, $C_1.$ This computation is

possible using the following expression:

$N_1=\frac{N_A{C}_1}{\frac{C_1{A}_1}{{}_1}+\frac{A_1}{{}_2}(100-C_1)}$

Where

$N_A=$ Avogadro's number

${}_1$ and ${}_2=$ densities of the two elements

$A_1=$ the atomic weight of element $1$

Derive the aforementioned equation using the following equation:

$($:$N=\frac{N_A{}_{\text{a}\text{v}\text{e}}}{A_{\text{a}\text{v}\text{e}}},i$