13.041. A 30% hydrochloric acid solution was mixed with a 10% solution to obtain 600 g of a 15% solution. How many grams of each solution were taken?
## Solution.

Let $x$ g of a $30\%$ hydrochloric acid solution and $(600-x)$ g of a $10\%$ solution be taken. The mass of hydrochloric acid in the $30\%$ solution is $0.3x$ g; in the $10\%$ solution, it is $0.1(600-x)$ g. In the resulting $15\%$ solution, the mass of hydrochloric acid is $0.15 \cdot 600 = 90$ g. According to the condition, $0.3x + 0.1(600-x) = 90$, from which $x = 150$ g of the $30\%$ solution; $600 - 150 = 450$ g of the $10\%$ solution.

Answer: 150 and 450 g.