Mixing sugar syrups to target 10% concentration: Solution A is 15% sugar; solution B is 5% sugar. How many liters of solution B must be added to 20 L of solution A to obtain a 10% sugar mixture?

Introduction / Context: Use sugar mass balance: sugar from A plus sugar from B must equal 10% of the total final volume. One linear equation in the unknown liters of B is sufficient to solve the problem cleanly and exactly.

Given Data / Assumptions:

• A: 20 L at 15% ⇒ sugar = 3 L.
• B: x L at 5% ⇒ sugar = 0.05x L.
• Final: (20 + x) L at 10% ⇒ sugar = 0.10(20 + x) L.

Concept / Approach: Set 3 + 0.05x = 0.10(20 + x) and solve for x. This equates total sugar before and after mixing.

Step-by-Step Solution:

Verification / Alternative check: Final volume 40 L; sugar = 3 + 1 = 4 L ⇒ 4/40 = 10%, as required.

Why Other Options Are Wrong: 10 L or 15 L would yield sugar fractions above 10%; 5 L is too small; only 20 L balances at exactly 10%.

Common Pitfalls: Averaging percentages instead of doing mass balance; forgetting to convert percent to fractions in equations.

Final Answer: 20 L