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Finding the Third Proportional to 13,222 and 20,497

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Solution

The third proportional to 13,222 and 20,497 is: 31,774.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,222 : 20,497 = 20,497 : x
  2. Step 2: Convert to fraction form
    13,222/20,497 = 20,497/x
  3. Step 3: Cross multiply
    13,222x = 20,497 × 20,497
  4. Step 4: Simplify right side
    13,222x = 420,127,009
  5. Step 5: Solve for x
    x = 420,127,009/13,222
  6. Step 6: Final answer
    x = 31,774.85

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.