Determine the mass fraction of sodium hydroxide in the solution formed when draining 100 g of 40%

Determine the mass fraction of sodium hydroxide in the solution formed when draining 100 g of 40% and 150 g of 20% solutions.

Given:
W1 = 40%
m solution 1 = 100 g
W2 = 20%
m solution 2 = 150 g
Find:
W3 (NaOH) =?
Solution:
1) Let’s write the formulas that we will use.
W = (m substance: m solution) x 100%
m substance = (W x m solution): 100%
2) m of substance 1 = (40% x 100 g): 100% = 40 g.
m of substance 2 = (20% x 150 g): 100% = 30 g.
3) m substance 3 = m substance 1 + m substance 2
m of substance 3 = 40 g + 30 g = 70 g
4) m solution 3 = m solution 1 + m solution 2
m solution 3 = 100 g + 150 g = 250 g
5) W3 = (70: 250) x 100% = 28%
Answer: W3 (NaOH) = 28%