Calculate the mass fraction of a substance in a solution obtained by dissolving 150 g

Calculate the mass fraction of a substance in a solution obtained by dissolving 150 g of sodium chloride in 350 g of a 15% solution of the same salt.

Given:
m2 (NaCl) = 150 g
m1 solution (NaCl) = 350 g
ω1 (NaCl) = 15%

Find:
ω3 (NaCl) -?

Solution:
1) Calculate the mass of NaCl in the original solution:
m1 (NaCl) = ω1 (NaCl) * m1 solution (NaCl) / 100% = 15% * 350/100% = 52.5 g;
2) Calculate the mass of NaCl in the resulting solution:
m3 (NaCl) = m1 (NaCl) + m2 (NaCl) = 52.5 + 150 = 202.5 g;
3) Calculate the mass of the resulting NaCl solution:
m3 solution (NaCl) = m1 solution (NaCl) + m2 (NaCl) = 350 + 150 = 500 g;
4) Calculate the mass fraction of NaCl in the resulting solution:
ω3 (NaCl) = m3 (NaCl) * 100% / m3 solution (NaCl) = 202.5 * 100% / 500 = 40.5%.

Answer: The mass fraction of NaCl is 40.5%.