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.
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A121 : 39
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B131 : 49
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C39 : 121
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D49 : 131
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E12 : 4
Answer
Correct Answer: 121 : 39
Explanation
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:
Total milk = 1.8 + 4.0 + 6.3 = 12.1 L.Total water = 16 − 12.1 = 3.9 L.Milk : Water = 12.1 : 3.9 = 121 : 39.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