Keep in mind that regardless of how many they give each other, the total number of cards is the same.
Let The number of cards Amy have initially be 1u.
Amy received 22 cards from Bala.
Amy and Bala has (1u + 22) cards, since they have an equal number of cards.
Working backwards, Bala would have (1u + 22) + 22 = (1u + 44) cards

If Amy gave Bala 110 cards, Amy would left with
(1u - 110) cards.
Bala would end up with 4 x (1u -110) = (4u - 440) cards.
Since total number of cards is the same,
1u + 1u + 44 = 1u - 110 + 4u - 440