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Finding the Third Proportional to 102,005 and 217,645

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Solution

The third proportional to 102,005 and 217,645 is: 464,382.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,005 : 217,645 = 217,645 : x
  2. Step 2: Convert to fraction form
    102,005/217,645 = 217,645/x
  3. Step 3: Cross multiply
    102,005x = 217,645 × 217,645
  4. Step 4: Simplify right side
    102,005x = 47,369,346,025
  5. Step 5: Solve for x
    x = 47,369,346,025/102,005
  6. Step 6: Final answer
    x = 464,382.59

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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.