We merged 2 salt solutions: 100 g of a 15% salt solution and 250 g of a 10% solution of the same salt.

We merged 2 salt solutions: 100 g of a 15% salt solution and 250 g of a 10% solution of the same salt. What is the mass fraction of the new solution?

Given:
m1 solution = 100 g
m2 solution = 250 g
w1 = 15% = 0.15
w2 = 10% = 0.1
Find: w3
Decision:
m3 solution = 100 g + 250 g = 350 g
Let x – w3, then
(m1 solution * 0.15) + (m2 solution * 0.1) = m3 solution * x
(100 * 0.15) + (250 * 0.1) = 350x
15 + 25 = 350x
40 = 350x
x = 0.1143 / * 100%
w3 = 11.43%
Answer: 11.43%