There are two alloys with different iron contents. In the first alloy, 20%, and in the second – 45% iron.

There are two alloys with different iron contents. In the first alloy, 20%, and in the second – 45% iron. In what relation should the first and second alloys be taken, what to get from them a new alloy containing 30% iron?

1. Quantity of the first alloy: M1 kg;

2. The concentration of iron in it: K1 = 20% or K1 = 0.2;

3. The amount of the second alloy: M2 kg;

4. Iron concentration: K2 = 45% or K2 = 0.45;

5. The new alloy has a mass: M kg;

6. The concentration of iron in it: K = 30% or K = 0.3;

7. Iron balance:

K1 * M1 + K2 * M2 = K * M;

0.2 * M1 + 0.45 * M2 = 0.3 * (M1 + M2);

(0.45 – 0.3) * M2 = (0.3 – 0.2) * M1;

0.15 * M2 = 0.1 * M1;

8. Ratio: M1 / M2 = 0.15 / 0.1 = 3/2.

Answer: the first and second alloys should be taken in a ratio of 3/2.