Solutions A and B are mixtures of milk and water. Solutions A and B contain milk and water in the ratio 3 : 5 and 1 : 2 respectively. When A and B are mixed in the ratio 2 : 1, the quantities of milk and water in the resulting mixture differ by 5 litres. Find the quantity of milk in the resulting mixture.5ℓ5.5ℓ6ℓ6.5ℓ
Question
Solutions A and B are mixtures of milk and water. Solutions A and B contain milk and water in the ratio 3 : 5 and 1 : 2 respectively. When A and B are mixed in the ratio 2 : 1, the quantities of milk and water in the resulting mixture differ by 5 litres. Find the quantity of milk in the resulting mixture.5ℓ5.5ℓ6ℓ6.5ℓ
Solution
Let's denote:
- The quantity of milk in solution A as 3x and the quantity of water as 5x.
- The quantity of milk in solution B as y and the quantity of water as 2y.
When solutions A and B are mixed in the ratio 2:1, the total quantity of milk is 2*(3x) + 1y = 6x + y, and the total quantity of water is 2(5x) + 1*(2y) = 10x + 2y.
According to the problem, the quantities of milk and water in the resulting mixture differ by 5 litres. Therefore, we can write the equation:
10x + 2y - (6x + y) = 5 4x + y = 5
We don't have enough information to solve this equation for x and y. The problem might be missing some information or there might be a mistake in the problem statement.
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