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Finding the Third Proportional to 38,678 and 82,414

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Solution

The third proportional to 38,678 and 82,414 is: 175,605.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,678 : 82,414 = 82,414 : x
  2. Step 2: Convert to fraction form
    38,678/82,414 = 82,414/x
  3. Step 3: Cross multiply
    38,678x = 82,414 × 82,414
  4. Step 4: Simplify right side
    38,678x = 6,792,067,396
  5. Step 5: Solve for x
    x = 6,792,067,396/38,678
  6. Step 6: Final answer
    x = 175,605.44

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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.