## 41. Lift

Three sisters are standing in line at a ski lift on a mountain slope together with their instructor. Out of boredom, he asked the oldest sister how old they are.

- I'll only say, - she replied, - that if you subtract nine times the age of my youngest sister from the product of my age and the age of my middle sister, you get 89.

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-076.jpg?height=517&width=1176&top_left_y=284&top_left_x=454)

The instructor remembered that the middle sister had just updated her skis and that her parents had given them to her on her tenth birthday. Then he easily determined the age of each of the sisters.

Can you do it?
41. So, the elder sister is over 10 years old, the middle one is exactly 10 years old, and the younger one is less than 10 years old. Let $a$ be the age of the elder sister, and $b$ be the age of the younger sister.

According to the problem,

$$
10 a-9 b=89
$$

or

$$
10(a-b)+b=10 \cdot 8+9
$$

Therefore,

$$
a-b=8 \text { and } b=9
$$

Thus, the younger sister is 9 years old, the middle one is 10 years old, and the elder one is 17 years old.