## PROBLEM 3

Six years ago, the daughter's age was equal to 0.2 of the mother's age, and in 9 years, the daughter's age will be 0.5 of the age the mother will have. How old is each one currently?
## Solution:

Establishing the unknowns: $f$ - the daughter's current age and $m$ - the mother's current age, and forming the relationships

![](https://cdn.mathpix.com/cropped/2024_06_07_6a3c6f667f5f63465e11g-3.jpg?height=74&width=1408&top_left_y=637&top_left_x=241)

Express the unknown $f$ from both relationships: $f=\frac{m-6}{5}+6$ and $f=\frac{m+9}{2}-9 \ldots . . .2$ points

Equating them, we get $\frac{m-6}{5}+6=\frac{m+9}{2}-9 \Rightarrow m=31$ years 2 points

Thus, $f=\frac{m-6}{5}+6=11$ years

1 point