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Finding the Third Proportional to 83,539 and 197,137

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Solution

The third proportional to 83,539 and 197,137 is: 465,207.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,539 : 197,137 = 197,137 : x
  2. Step 2: Convert to fraction form
    83,539/197,137 = 197,137/x
  3. Step 3: Cross multiply
    83,539x = 197,137 × 197,137
  4. Step 4: Simplify right side
    83,539x = 38,862,996,769
  5. Step 5: Solve for x
    x = 38,862,996,769/83,539
  6. Step 6: Final answer
    x = 465,207.83

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.