We merged two salt solutions: 100 g of 20% and 450 g of 10%. Calculate the mass fraction of salt in the new solution.

Given:
m1 solution (salt) = 100 g
ω1 (salt) = 20%
m2 solution (salt) = 450 g
ω2 (salt) = 10%

To find:
ω3 (salt) -?

Decision:
1) m1 (salts) = ω1 (salts) * m1 solution (salts) / 100% = 20% * 100/100% = 20 g;
2) m2 (salt) = ω2 (salt) * m2 solution (salt) / 100% = 10% * 450/100% = 45 g;
3) m3 (salt) = m1 (salt) + m2 (salt) = 20 + 45 = 65 g;
4) m3 solution (salt) = m1 solution (salt) + m2 solution (salt) = 100 + 450 = 550 g;
5) ω3 (salt) = m3 (salt) * 100% / m3 solution (salt) = 65 * 100% / 550 = 11.8%.

Answer: The mass fraction of salt is 11.8%.