Mixed 100 grams of a solution with a mass fraction of a substance of 20% and 50 grams of a solution with a mass fraction

Mixed 100 grams of a solution with a mass fraction of a substance of 20% and 50 grams of a solution with a mass fraction of this substance of 32%, calculate the mass fraction of a solute in the newly obtained solution.

Given:
m1 solution (in-va) = 100 g
ω1 (in-va) = 20%
m2 solution (in-va) = 50 g
ω2 (in-va) = 32%

To find:
ω3 (in-va) -?

Solution:
1) m1 (in-va) = ω1 (in-va) * m1 solution (in-va) / 100% = 20% * 100/100% = 20 g;
2) m2 (in-va) = ω2 (in-va) * m2 solution (in-va) / 100% = 32% * 50/100% = 16 g
3) m3 (in-va) = m1 (in-va) + m2 (in-va) = 20 + 16 = 36 g;
4) m3 solution (in-va) = m1 solution (in-va) + m2 solution (in-va) = 100 + 50 = 150 g;
5) ω3 (in-va) = m3 (in-va) * 100% / m3 solution (in-va) = 36 * 100% / 150 = 24%.

Answer: The mass fraction of the substance is 24%.