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Finding the Third Proportional to 9,834 and 21,234

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Solution

The third proportional to 9,834 and 21,234 is: 45,849.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,834 : 21,234 = 21,234 : x
  2. Step 2: Convert to fraction form
    9,834/21,234 = 21,234/x
  3. Step 3: Cross multiply
    9,834x = 21,234 × 21,234
  4. Step 4: Simplify right side
    9,834x = 450,882,756
  5. Step 5: Solve for x
    x = 450,882,756/9,834
  6. Step 6: Final answer
    x = 45,849.38

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.