A mixture problem is a weighted sum: each part times its rate, added together, equals the final amount times the final rate. The setup is the whole question. Word-problem structure is in setting up word problems.
The equation
4 liters of a 10% solution mixed with 6 liters of a 30% solution gives (4)(0.10) + (6)(0.30) = 10x. Then 0.4 + 1.8 = 10x, so x = 0.22. The result is 22%, which is between 10 and 30 and closer to 30 because there is more of that solution. If the answer is outside the two starting percents, the arithmetic is wrong.
Percent language around the rates is in percent problems.
Keep the units on one system
Liters with liters, or convert first. Mixing grams and kilograms in the same equation will not balance. Conversions are in unit conversions. Rate problems that are about speed rather than concentration are in rate problems.
The bottom line
Amount times strength, added, equals total amount times final strength. The answer sits between the two starting strengths.
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