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Assume the percentages of the two salt solutions \(A\) and \(B\) are \(a%\) and \(b%\), respectively. We need to figure out the amount of salt for salt solution questions.
The amount of salt in \(200g\) of solution \(A\) is \(200*(\frac{a}{100}) = 2a\). The amount of salt in \(100g\) of solution \(B\) is \(100*(\frac{b}{100}) = b.\)
After mixing the \(2\) solutions, the new solution is \(\frac{(2a + b) }{ 300} = \frac{4}{100}\), \(100(2a + b) = 4(300),\) and \(200a + 100b = 1200\). Dividing everything by \(100\) gives us \(2a + b = 12.\)
Then, the amount of salt in \(100g\) of solution \(A\) is \(100*(\frac{a}{100}) = a\) and \(200*(\frac{b}{100}) = 2b.\)
After mixing the \(2\) solution, the new solution is \(\frac{(a + 2b) }{ 300} = \frac{3}{100,} 100(a + 2b) = 3(300),\) and \(100a + 200b = 900\). Dividing everything by \(100\) gives us \(a + 2b = 9.\)
When we add two equations, we have \((2a + b) + (a + 2b) = 12 + 9, 3a + 3b = 21\) or \(a + b = 7.\)
Then we have \(a = (2a + b) - (a + b) = 12 – 7 = 5\) and \(b = (a + 2b) – (a + b) = 9 – 7 = 2.\)
Therefore, A is the answer
Answer: A
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