## 16. Grandmother, the Mark, and the Kittens

If you write down my mark, which I received in school for Latin ${ }^{1}$, twice in a row, you will get my grandmother's age. And what would you get if you divide this age by the number of my kittens? Imagine this - you would get my morning mark, increased by fourteen thirds?

How old is my grandmother?
16. Let $a$ be the age of my grandmother, $c$ be the number of my kittens, and $l$ be my grade in Latin. From the first condition of the problem, it follows that $l$ is an integer less than 10 (since it is clear that the age of my grandmother is less than 1010 years), and that $a=11 l$.

The second condition of the problem can be written as the equation

$$
a / c=3 l+14 / 3,
$$

or

$$
a=3 c l+14 c / 3 \text { . }
$$

Thus, $c$ is a multiple of 3; and since $3 c$ must be less than 11, $c$ equals 3. Therefore, we have

$$
a=11 l \text { and } a=9 l+14 \text {, }
$$

from which it is easy to find

$$
l=7, \quad a=77
$$

Thus, my grandmother is 77 years old.