Question

Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{part}\mathrm{of}184\mathrm{be}\mathrm{x}. \\ \mathrm{Therefore},\mathrm{the}\mathrm{other}\mathrm{part}\mathrm{will}\mathrm{be}(184-\mathrm{x}). \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ \frac{1}{3}\mathrm{x}-\frac{1}{7}(184-\mathrm{x})=8 \\ \mathrm{or}\frac{7\mathrm{x}-552+3\mathrm{x}}{21}=8 \\ \mathrm{or}10\mathrm{x}-552=168[\text{After c}\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}10\mathrm{x}=168+552 \\ \mathrm{or}\mathrm{x}=\frac{720}{10}=72 \\ \mathrm{Thus},\mathrm{the}\mathrm{parts}\mathrm{of}184\mathrm{are}72\mathrm{and}112(184-72=112). \end{gathered}$$