Combining three mixtures with different milk strengths: Glasses of 2 L (90% milk), 5 L (80% milk), and 9 L (70% milk) are poured into one vessel. Find the milk concentration and the milk:water ratio in the final mixture.

Introduction / Context: To combine different concentrations, compute absolute milk volumes from each container, add them, and compare against the total volume to get both concentration and milk:water ratio.

Given Data / Assumptions:

• 2 L at 90% ⇒ milk = 1.8 L.
• 5 L at 80% ⇒ milk = 4.0 L.
• 9 L at 70% ⇒ milk = 6.3 L.
• Total volume = 16 L.

Concept / Approach: Sum milk volumes to get total milk; water is total minus milk. Ratio milk:water yields an integer pair on scaling (here by 10).

Step-by-Step Solution:

Verification / Alternative check: Milk fraction = 12.1/16 = 0.75625 = 75.625%; consistent with ratio 121 : 39 since 121/(121+39) = 121/160 = 75.625%.

Why Other Options Are Wrong: 131 : 49 or 49 : 131 correspond to different milk totals; 39 : 121 inverts the ratio.

Common Pitfalls: Averaging percentages directly; always convert to absolute amounts before combining.

Final Answer: 121 : 39