8.4. Masha and Katya wove wreaths from wildflowers: dandelions, cornflowers, and daisies. The total number of flowers in the wreaths of both girls turned out to be 70, with dandelions making up $5 / 9$ of Masha's wreath, and daisies making up 7/17 of Katya's wreath. How many cornflowers are in each girl's wreath, if the number of dandelions and daisies is the same for both?
Answer: Masha has 2 cornflowers in her wreath, while Katya has no cornflowers.

Solution. From the condition, it follows that Masha has a total of $9 n$ flowers in her wreath, and Katya has $-17 k$, where $n$ and $k$ are non-negative integers. Then, in the girls' wreaths, there are $5 n$ daisies and $7 k$ chamomiles. Since there are a total of 70 flowers in the wreaths, we get the equation $9 n + 17 k = 70$.

Thus, 70 - 17k must be divisible by 9. By trial, we find that only $k=2$ fits, from which $n=4$. This means Masha has 36 flowers in her wreath, and Katya has 34. Then, in each wreath, there are $5 n = 20$ daisies and $7 k = 14$ chamomiles, so Masha has 2 cornflowers in her wreath, while Katya has no cornflowers.