68. Parrots on Two Trees Two trees are occupied by some parrots.The parrots on the first tree say:“If one parrot from the second tree flies over to our tree, both trees will have the same number of parrots.”The parrots on the second tree reply:“Instead, if one parrot from the first tree flies to our tree, we will have exactly twice as many parrots as the first tree.”How many parrots are perched on each tree? Added 24 October 2013 Show Hint Show Solution Hint: Set up two equations: let x be the number on the first tree and y on the second. Translate each statement directly into an equation. Solution: Let x = parrots on the first tree, y = parrots on the second tree.1. If one parrot moves from the second to the first tree:(x + 1) = (y − 1)2. If one parrot moves from the first to the second tree:(y + 1) = 2 (x − 1)From (1): y = x + 2.Substitute into (2):(x + 2) + 1 = 2(x − 1)x + 3 = 2x − 25 = xHence y = x + 2 = 7.Answer: 5 parrots on the first tree and 7 parrots on the second tree.
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