6. Increase Grisha's catch by $40 \%$ and Vasya's catch by $20 \%$.

Grisha, the most resourceful of them, calculated that their total catch in each case would increase by 5, 10, and 9 kg respectively. What was the total catch of the friends (in kilograms) before meeting with Shapka?
Answer: 40.

Solution. Let the harvest of Vasya, Misha, and Grisha be denoted by $x, y, z$ respectively. Then, $0.4 x + 0.2 y = 5 ; 0.4 y + 0.2 z = 10 ; 0.4 z + 0.2 x = 9$. Adding the equations, we get $0.6(x + y + z) = 24$, from which $x + y + z = 40$.