Question

At a party, colas, squash and fruit juice were offered to guests. A fourth of the guests drank colas, a third drank squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{guests}\mathrm{be}\mathrm{x}. \\ \mathrm{Therefore},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{guests},\mathrm{who}\mathrm{drank}\mathrm{colas},\mathrm{would}\mathrm{be}\frac{1}{4}\mathrm{x}. \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{guests},\mathrm{who}\mathrm{drank}\mathrm{squash},\mathrm{would}\mathrm{be}\frac{1}{3}\mathrm{x}. \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{guests},\mathrm{who}\mathrm{drank}\mathrm{fruit}\mathrm{juice},\mathrm{would}\mathrm{be}\frac{2}{5}\mathrm{x}. \\ \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{guests},\mathrm{who}\mathrm{did}\mathrm{not}\mathrm{drink},\mathrm{would}\mathrm{be}3. \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}, \\ \mathrm{x}-(\frac{\mathrm{x}}{4}+\frac{\mathrm{x}}{3}+\frac{2\mathrm{x}}{5})=3 \\ \mathrm{or}\frac{60\mathrm{x}-15\mathrm{x}-20\mathrm{x}-24\mathrm{x}}{60}=3 \\ \mathrm{or}\mathrm{x}=180 \\ \mathrm{Thus},\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{guests}=180. \end{gathered}$$