## 28. At the Ball

When I saw Eleanor, I found her very pretty. After a brief banal conversation, I told her how old I was and asked about her age. She replied:

- When you were as old as I am now, you were three times as old as I was. When I am three times as old as I am now, together we will be exactly a century old.

I didn't understand a word of this gibberish and told her so. Then she decided that I didn't deserve her attention and left without giving me an answer.

How old is this stubborn creature?
28. So, let's turn to the conversation of two individuals. Let $e-$ be Eleonora's age, and $m$ - my age. When I was as old as she is now, Eleonora's age was

$$
e-(m-e)=2 e-m .
$$

Therefore, from her first statement, the following equality follows:

$$
e=3(2 e-m) \text{, or } 3 m=5 e \text{. }
$$

When Eleonora becomes three times as old as she is now, I will be

$$
m+(3 e-e)=m+2 e
$$

years old. From Eleonora's second statement, it follows that

$$
3 e+(m+2 e)=100 \text{, or } 5 e+m=100 \text{. }
$$

Considering the first equation, we get

$$
3 m+m=100 \text{, or } m=25 \text{. }
$$

Therefore,

$$
e=3 m / 5=15
$$

So, Eleonora is 15 years old.