Mixed 200 and 300 kg of solutions with a mass fraction of a solute, respectively, 50 and 20%

Mixed 200 and 300 kg of solutions with a mass fraction of a solute, respectively, 50 and 20%. Determine the mass fraction of the solute in the resulting solution.

Given:
m1 solution (in-va) = 200 kg
m2 solution (in-va) = 300 kg
ω1 (in-va) = 50%
ω2 (in-va) = 20%

To find:
ω3 (in-va) -?

Decision:
1) m1 (in-va) = ω1 (in-va) * m1 solution (in-va) / 100% = 50% * 200/100% = 100 kg;
2) m2 (in-va) = ω2 (in-va) * m2 solution (in-va) / 100% = 20% * 300/100% = 60 kg
3) m3 (in-va) = m1 (in-va) + m2 (in-va) = 100 + 60 = 160 kg;
4) m3 solution (in-va) = m1 solution (in-va) + m2 solution (in-va) = 200 + 300 = 500 kg;
5) ω3 (in-va) = m3 (in-va) * 100% / m3 solution (in-va) = 160 * 100% / 500 = 32%.

Answer: The mass fraction of the substance is 32%.