Mixed 30% and 50% solutions of nitric acid by weight and received a 45% solution.

Mixed 30% and 50% solutions of nitric acid by weight and received a 45% solution. Find the ratio of the mass of a 30% solution to the mass of a 50% solution.

1. Concentration of the first solution: K1 = 30% = 0.3;

2. The mass of this solution is: M1 kg;

3. Concentration of the second solution: K2 = 50% = 0.5;

4. The mass of this solution: M2 kg;

5. Concentration of the new solution: K3 = 45% = 0.45;

6. Its mass is equal to: M3 = (M1 + M2) kg;

7. Let’s write in mathematical language the process of preparing a new solution:

0.3 * M1 + 0.5 * M2 = 0.45 * M3;

0.3 * M1 + 0.5 * M2 = 0.45 * (M1 + M2);

0.3 * M1 + 0.5 * M2 = 0.45 * M1 + 0.45 * M2;

M2 * (0.5 – 0.45) = M1 * (0.45 – 0.3);

0.05 * M2 = 0.15 * M1;

8. The ratio of the masses of the initial solutions:

M1 / M2 = 0.05 / 0.15 = 1/3.

Answer: the ratio of the masses of the solutions is 1/3.