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Finding the Third Proportional to 9,709 and 20,689

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Solution

The third proportional to 9,709 and 20,689 is: 44,086.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,709 : 20,689 = 20,689 : x
  2. Step 2: Convert to fraction form
    9,709/20,689 = 20,689/x
  3. Step 3: Cross multiply
    9,709x = 20,689 × 20,689
  4. Step 4: Simplify right side
    9,709x = 428,034,721
  5. Step 5: Solve for x
    x = 428,034,721/9,709
  6. Step 6: Final answer
    x = 44,086.39

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.