Question

Four-fifths of a number is 10 more than two-thirds of the number. Find the number.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Four}\mathrm{fifths}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{is}10\mathrm{more}\mathrm{than}\mathrm{two}\mathrm{thirds}\mathrm{of}\mathrm{the}\mathrm{number}. \\ \therefore \frac{4}{5}x=10+\frac{2}{3}x \\ \Rightarrow \frac{4x}{5}=10+\frac{2x}{3} \\ \Rightarrow \frac{4x}{5}=\frac{30+2x}{3}(L.C.M.\hspace{0.17em}\mathrm{of}1\mathrm{and}3\mathrm{is}3) \\ \Rightarrow 3\left(4x\right)=5(30+2x)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 12x=150+10x \\ \Rightarrow 12x-10x=150 \\ \Rightarrow 2x=150 \\ \Rightarrow x=\frac{150}{2}=75 \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{is}75. \end{gathered}$$