## Task 2 - 200712

From an ancient Egyptian arithmetic book (1700 BC) comes the following problem:

A traveler notices that a shepherd is leading 70 sheep to pasture. He asks the shepherd: "Are the sheep you are leading here all of your sheep?"

"No," the shepherd replies, "I am only leading two-thirds of a third of the entire herd entrusted to me to pasture."

Determine the total number of sheep in the entire herd entrusted to this shepherd!
If $x$ is the total number of the herd, then one third of the herd is $\frac{x}{3}$, and two thirds of this third are $\frac{2}{3} \cdot \frac{x}{3}$. Therefore, according to the problem statement:

$$
\frac{2}{3} \cdot 13=70 \quad \text { so } \quad x=315
$$

The total number of the herd is therefore 315.