What was the mass fraction of potassium in its mixture with lithium if, as a result of the treatment of this mixture

What was the mass fraction of potassium in its mixture with lithium if, as a result of the treatment of this mixture with an excess of chlorine, a mixture was formed in which the mass fraction of potassium chloride was 80%?

Given:
mixture (K, Li)
ω (KCl) = 80%

To find:
ω (K) -?

Decision:
1) 2K + Cl2 => 2KCl;
2Li + Cl2 => 2LiCl;
2) Let m mixture (KCl, LiCl) = 100 g;
3) m (KCl) = ω (KCl) * m mixture (KCl, LiCl) / 100% = 80% * 100/100% = 80 g;
4) m (LiCl) = m mixture (KCl, LiCl) – m (KCl) = 100 – 80 = 20 g;
5) n (KCl) = m (KCl) / M (KCl) = 80 / 74.5 = 1.07 mol;
6) n (LiCl) = m (LiCl) / M (LiCl) = 20 / 42.5 = 0.47 mol;
7) n (K) = n (KCl) = 1.07 mol;
8) n (Li) = n (LiCl) = 0.47 mol;
9) m (K) = n (K) * M (K) = 1.07 * 39 = 41.73 g;
10) m (Li) = n (Li) * M (Li) = 0.47 * 7 = 3.29 g;
11) m mixture (K, Li) = m (K) + m (Li) = 41.73 + 3.29 = 45.02 g;
12) ω (K) = m (K) * 100% / m mixture (K, Li) = 41.73 * 100% / 45.02 = 92.7%.

Answer: Mass fraction of K is 92.7%.