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Finding the Third Proportional to 10,306 and 11,782

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Solution

The third proportional to 10,306 and 11,782 is: 13,469.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,306 : 11,782 = 11,782 : x
  2. Step 2: Convert to fraction form
    10,306/11,782 = 11,782/x
  3. Step 3: Cross multiply
    10,306x = 11,782 × 11,782
  4. Step 4: Simplify right side
    10,306x = 138,815,524
  5. Step 5: Solve for x
    x = 138,815,524/10,306
  6. Step 6: Final answer
    x = 13,469.39

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.