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Finding the Third Proportional to 83,909 and 128,051

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Solution

The third proportional to 83,909 and 128,051 is: 195,414.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,909 : 128,051 = 128,051 : x
  2. Step 2: Convert to fraction form
    83,909/128,051 = 128,051/x
  3. Step 3: Cross multiply
    83,909x = 128,051 × 128,051
  4. Step 4: Simplify right side
    83,909x = 16,397,058,601
  5. Step 5: Solve for x
    x = 16,397,058,601/83,909
  6. Step 6: Final answer
    x = 195,414.78

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.