Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. Two identical containers, X and Y, each have a capacity of x liters. Initially, Container X is \(\frac{4}{5}\) full of water and Container Y is full as well. If 4 liters of water are transferred from Container X to Container Y, the amount of water in Container X becomes \(\frac{2}{3}\) of the amount in Container Y. Find the capacity x of each container.
Explanation: (C) Initial water in X: \(\frac{4}{5}x\). Initial water in Y: \(\frac{4}{5}x\). After transfer: Water in X = \(\frac{4}{5}x - 4\). Water in Y = \(\frac{4}{5}x + 4\). Condition: \(\frac{4}{5}x - 4 = \frac{2}{3} \cdot (\frac{4}{5}x + 4)\). Multiplying by 15: \(15 \cdot (\frac{4}{5}x - 4) = 15 \cdot \frac{2}{3} \cdot (\frac{4}{5}x + 4) \implies 12x - 60 = 10 \cdot (\frac{4}{5}x + 4) \implies 12x - 60 = 8x + 40\). \(4x = 100 \implies x = 25\).
