How many grams of a 25% by mass solution of KOH should be added to 400 ml of water to obtain a 15% by mass solution?

Given:
ω1 (KOH) = 25%
V (H2O) = 400 ml
ω2 (KOH) = 15%

To find:
m1 solution (KOH) -?

Solution:
1) Let m1 solution (KOH) = (x) z;
2) m1 (KOH) = ω1 (KOH) * m1 solution (KOH) / 100% = 25% * x / 100% = (0.25x) g;
3) m2 (KOH) = m1 (KOH) = (0.25x) g;
4) m (H2O) = ρ (H2O) * V (H2O) = 1 * 400 = 400 g;
5) m2 solution (KOH) = m1 solution (KOH) + m (H2O) = (x + 400) g;
6) ω2 (KOH) = m2 (KOH) * 100% / m2 solution (KOH);
15% = 0.25x * 100% / (x + 400);
x = 600;
7) m1 solution (KOH) = x = 600 g.

Answer: The mass of the KOH solution is 600 g.