Question

Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{one}\mathrm{part}\mathrm{be}\mathrm{x}. \\ 7\mathrm{times}\mathrm{the}\mathrm{first}\mathrm{part}=7\mathrm{x} \\ \mathrm{Let}\mathrm{the}\mathrm{other}\mathrm{part}\mathrm{be}(24-\mathrm{x}). \\ 5\mathrm{times}\mathrm{the}\mathrm{second}\mathrm{part}=5(24-\mathrm{x}) \\ \therefore 7x+5(24-x)=146 \\ \Rightarrow 7x+120-5x=146 \\ \Rightarrow 7x-5x=146-120 \\ \Rightarrow 2x=26 \\ \Rightarrow x=\frac{26}{2}=13 \\ \mathrm{Therefore},\mathrm{one}\mathrm{part}\mathrm{is}13. \\ \hspace{0.17em}\mathrm{Other}\mathrm{part}=(24-x)=(24-13)=11 \end{gathered}$$