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Finding the Third Proportional to 102,684 and 206,893

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Solution

The third proportional to 102,684 and 206,893 is: 416,858.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,684 : 206,893 = 206,893 : x
  2. Step 2: Convert to fraction form
    102,684/206,893 = 206,893/x
  3. Step 3: Cross multiply
    102,684x = 206,893 × 206,893
  4. Step 4: Simplify right side
    102,684x = 42,804,713,449
  5. Step 5: Solve for x
    x = 42,804,713,449/102,684
  6. Step 6: Final answer
    x = 416,858.65

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Why These Related Problems?

These problems maintain the same ratio (2.01) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.