## Precalculus (6th Edition) Blitzer

The percentage of population: capitalist $C=1\%$ %, upper-middle class $U=15$ %, lower-middle class $L=34\%$ %and working class $W=30\%$ %
Let C be the capitalist percentage. Let U be the upper-middle class percentage. Let L be the lower-middle class percentage. Let W be the working class percentage. From the given relation, we get: $C+U+W+L=80$ (I) $L-\left( C+U \right)=18$ (II) $L-W=4$ (III) $3U-\left( C+L \right)=10$ (IV) Add (I) and (II) as below: \begin{align} & C+U+W+L+L-\left( C+U \right)=80+18 \\ & W+2L=98 \end{align} (V) Add (III) and (V) as below: \begin{align} & \left( W+2L \right)+L-W=\left( 98 \right)+\left( 4 \right) \\ & 3L=102 \\ & L=34 \\ \end{align} Substitute the above value in (V) as below: \begin{align} & W+2L=98 \\ & W+\left( 2 \right)\times \left( 34 \right)=98 \\ & W+68=98 \\ & W=30 \end{align} Substitute both the values in (I) as below: \begin{align} & C+U+W+L=80 \\ & C+U+30+34=80 \\ & C+U+64=80 \\ & C+U=16 \end{align} (VI) Add (II) and (IV) as below: \begin{align} & L-\left( C+U \right)+3U-\left( C+L \right)=18+10 \\ & -2C+2U=28 \\ & U-C=14 \end{align} (VII) Add (VI) and (VII) as below: \begin{align} & C+U+U-C=16+14 \\ & 2U=30 \\ & U=15 \end{align} And \begin{align} & U-C=14 \\ & 15-C=14 \\ & C=1 \end{align}