## 7. Bats, bears, poodles, and elephants

Attentive naturalists have established that the daily diet of 17 bears matches the diet of 170 poodles, the diet of 100000 bats matches the diet of

50 poodles, and 10 bears consume as much in a day as 4 elephants. How many bats can handle the diet of a dozen elephants?
7. Let $y$ be the daily diet of an elephant, $x$ be that of a bat, $z$ be that of a Pekingese, and $t$ be the daily diet of a bear. We know that

$$
17 t=170 z, \quad 100000 x=50 z, \quad 10 t=4 y,
$$

or

$$
t=10 z, \quad z=2000 x, \quad y=(5 / 2) t ;
$$

what we want to express is $y$ in terms of $x$. This is not difficult to do: it is clear that

$$
y=(5 / 2) \cdot 10 z=(5 / 2) \cdot 10 \cdot 2000 x=50000 x
$$

Therefore, a dozen elephants consume the same amount of food as 600,000 bats: $12 y=600000 x$.