The alloy of copper and zinc contains 20 kg of copper. When 25 kg of copper was added to the alloy, the percentage increased by 20%. Find the initial mass of the alloy.
1. Let’s designate the weight of zinc in the alloy through X.
2. Then the initial percentage of copper in the alloy will be:
20 * 100% / (20 + X).
3. After 25 kg of copper was added to the alloy, its percentage became equal to:
45 * 100% / (45 + X).
4. From the condition of the problem, we will compose the equation: 45 * 100% / (45 + X) – 20 * 100% / (20 + X) = 20%.
5. Multiply both sides of the equation by (20 + X) * (45 + X), perform arithmetic operations, simplify the expression. We get the quadratic equation: X ^ 2 – 60 * X + 900 = 0.
6. Note that this expression is the square of the difference between two numbers. I.e,
X ^ 2 – 60 * X + 900 = (X – 30) ^ 2 = 0.
7. This equation has a unique solution X = 30.
8. Then the initial mass of the alloy is 20 kg + 30 kg = 50 kg.
Answer: the initial mass of the alloy is 50 kg.
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