6.2. The lake is home to carp and perch. Two fishermen caught 70 fish, with 5/9 of the first fisherman's catch being carp, and 7/17 of the second fisherman's catch being perch. How many fish did each fisherman catch?
Solution. The number of fish caught by the second fisherman is a multiple of 17, so it can be: 17, 34, 51, or 68. The number of fish caught by the first can be (respectively) 53, 36, 19, or 2. But the number of fish caught by the first must be a multiple of 9, from which we get the answer: the first fisherman caught 36 fish, the second - 34.

Note that for this solution, it is not significant that the lake contains no fish other than carp and perch.

Answer. The catch is 36 fish and 34 fish.