**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?

**Solution:**

Let the total number of guests be $\mathrm{x}$.

Therefore, the number of guests, who drank colas, would be $\frac{1}{4} \mathrm{x}$.

The number of guests, who drank squash, would be $\frac{1}{3} \mathrm{x}$.

The number of guests, who drank fruit juice, would be $\frac{2}{5} \mathrm{x}$.

The number of guests, who did not drink, would be 3 .

According to the question,

$\mathrm{x}-\left(\frac{\mathrm{x}}{4}+\frac{\mathrm{x}}{3}+\frac{2 \mathrm{x}}{5}\right)=3$

or $\frac{60 \mathrm{x}-15 \mathrm{x}-20 \mathrm{x}-24 \mathrm{x}}{60}=3$

or $\mathrm{x}=180$

Thus, total number of guests $=180$.