How many grams of 80% H2SO4 solution do you need to add to 500 g of a 10% solution

How many grams of 80% H2SO4 solution do you need to add to 500 g of a 10% solution of the same substance to get a 30% solution?

Given:
ω1 (H2SO4) = 80%
m2 solution (H2SO4) = 500 g
ω2 (H2SO4) = 10%
ω3 (H2SO4) = 30%

To find:
m1 solution (H2SO4) -?

Decision:
1) Let m1 solution (H2SO4) = (x) z;
2) m1 (H2SO4) = ω1 (H2SO4) * m1 solution (H2SO4) / 100% = 80% * x / 100% = (0.8x) g;
3) m2 (H2SO4) = ω2 (H2SO4) * m2 solution (H2SO4) / 100% = 10% * 500/100% = 50 g;
4) m3 (H2SO4) = m1 (H2SO4) + m2 (H2SO4) = (0.8x + 50) g;
5) m3 solution (H2SO4) = m1 solution (H2SO4) + m2 solution (H2SO4) = (x + 500) g;
6) ω3 (H2SO4) = m3 (H2SO4) * 100% / m3 solution (H2SO4);
30% = (0.8x + 50) * 100% / (x + 500);
x = 200;
7) m1 solution (H2SO4) = x = 200 g.

Answer: The mass of the H2SO4 solution is 200 g.