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Finding the Third Proportional to 6,497 and 14,402

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Solution

The third proportional to 6,497 and 14,402 is: 31,925.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,497 : 14,402 = 14,402 : x
  2. Step 2: Convert to fraction form
    6,497/14,402 = 14,402/x
  3. Step 3: Cross multiply
    6,497x = 14,402 × 14,402
  4. Step 4: Simplify right side
    6,497x = 207,417,604
  5. Step 5: Solve for x
    x = 207,417,604/6,497
  6. Step 6: Final answer
    x = 31,925.14

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.