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Finding the Third Proportional to 12,431 and 14,591

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Solution

The third proportional to 12,431 and 14,591 is: 17,126.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,431 : 14,591 = 14,591 : x
  2. Step 2: Convert to fraction form
    12,431/14,591 = 14,591/x
  3. Step 3: Cross multiply
    12,431x = 14,591 × 14,591
  4. Step 4: Simplify right side
    12,431x = 212,897,281
  5. Step 5: Solve for x
    x = 212,897,281/12,431
  6. Step 6: Final answer
    x = 17,126.32

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.