## 14. Dromedaries ${ }^{1}$

Some of the dromedaries are sleeping, while others are awake; the number of sleeping dromedaries is seven eighths of the number of awake dromedaries plus another seven eighths of a dromedary. If half of the sleeping dromedaries woke up, the number of awake dromedaries would be between 25 and 65. And if all the sleeping dromedaries woke up, the number of awake dromedaries would be equal to...

Complete, please, the last sentence.
14. Let $d$ be the number of sleeping, and $r$ be the number of awake dromedaries. According to the problem, we have

$$
d=(7 / 8) r+7 / 8
$$

or

$$
8 d=7 r+7
$$

Thus, $d$ must be a multiple of 7.

On the other hand, this number must be such that it can be divided into two equal parts, i.e., it must be even; therefore, $d$ is divisible by 14. Further, we have the following possibilities:

| $d$ | 14 | 28 | 42 | 56 | and so on |
| :---: | :---: | :---: | :---: | :---: | :---: |
| $r$ | 15 | 31 | 47 | 63 | and so on |
| $r+d / 2$ | 22 | 45 | 68 | 91 | and so on |

In the third row of this table, the number of awake dromedaries is shown as it would be if half of the sleeping dromedaries woke up. Since, according to the problem, this number is between 25 and 65, it equals 45. Thus, $d=28$ and $r=31$. The total number of dromedaries is 59, which is what we needed to find.