The first alloy contains 5% copper, the second 13% copper. The mass of the second alloy is 4 kg

The first alloy contains 5% copper, the second 13% copper. The mass of the second alloy is 4 kg more than the mass of the first. From these two alloys, a third alloy containing 10% copper was obtained. Find the mass of the third alloy.

1. Let’s denote the weight of the first alloy through X kg, the weight of the second alloy through Y kg.

2. Then copper in the first alloy contains 0.05 * X kg, and in the second 0.13 * Y kg.

3. The first equation of the problem: Y = X + 4 (the second alloy is 4 kg heavier).

4. Second equation: (0.05 * X + 0.13 * Y) / (X + Y) = 0.1 (in the third alloy 10% copper).

5. Let’s multiply both sides of the second equation by (X + Y), combine the homogeneous terms.
We get: 5 * X – 3 * Y = 0.

6. Substitute the expression for Y from the first equation. We get: 2 * X = 12. That is, X = 6 kg.

7. Accordingly, Y = 6 kg + 4 kg = 10 kg.

8. The weight of the third alloy is the sum of the first and the second: X + Y = 6 kg + 10 kg = 16 kg.

Answer: the weight of the third alloy is 16 kg.