Calculate the mass fraction of salt in a solution formed from 100 g of an aqueous solution with a mass fraction

Calculate the mass fraction of salt in a solution formed from 100 g of an aqueous solution with a mass fraction of salt of 0.1 and 200 g of a solution with a mass fraction of the same salt of 0.4.

Given:
m1 solution (salt) = 100 g
ω1 (salt) = 0.1
m2 solution (salt) = 200 g
ω2 (salt) = 0.4

To find:
ω3 (salt) -?

Decision:
1) m1 (salt) = ω1 (salt) * m1 solution (salt) = 0.1 * 100 = 10 g;
2) m2 (salt) = ω2 (salt) * m2 solution (salt) = 0.4 * 200 = 80 g;
3) m3 (salt) = m1 (salt) + m2 (salt) = 10 + 80 = 90 g;
4) m3 solution (salt) = m1 solution (salt) + m2 solution (salt) = 100 + 200 = 300 g;
5) ω3 (salt) = m3 (salt) / m3 solution (salt) = 90/300 = 0.3.

Answer: The mass fraction of salt in the resulting solution is 0.3.