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Finding the Third Proportional to 13,497 and 31,523

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Solution

The third proportional to 13,497 and 31,523 is: 73,623.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,497 : 31,523 = 31,523 : x
  2. Step 2: Convert to fraction form
    13,497/31,523 = 31,523/x
  3. Step 3: Cross multiply
    13,497x = 31,523 × 31,523
  4. Step 4: Simplify right side
    13,497x = 993,699,529
  5. Step 5: Solve for x
    x = 993,699,529/13,497
  6. Step 6: Final answer
    x = 73,623.73

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.