What mass of a solution with a mass fraction of potassium hydroxide of 20% should be added to 1 kg of a solution

What mass of a solution with a mass fraction of potassium hydroxide of 20% should be added to 1 kg of a solution with a mass fraction of KOH of 50% to obtain a solution with a mass fraction of KOH of 25%?

Given:
ω1 (KOH) = 20%
m2 solution (KOH) = 1 kg
ω2 (KOH) = 50%
ω3 (KOH) = 25%

To find:
m1 solution (KOH) -?

1) To solve such a problem, the most optimal would be to use the cross rule (mixing rule, diagonal model of the “Pearson envelope”)
2) Calculate the mass of a 20% KOH solution, making the proportion:
5 kg of 50% KOH solution – 25 kg of 20% KOH solution;
1 kg of 50% KOH solution – x kg of 20% KOH solution;
m1 solution (KOH) = x = 1 * 25/5 = 5 kg.

Answer: The mass of the KOH solution is 5 kg.