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Finding the Third Proportional to 83,778 and 197,616

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Solution

The third proportional to 83,778 and 197,616 is: 466,137.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,778 : 197,616 = 197,616 : x
  2. Step 2: Convert to fraction form
    83,778/197,616 = 197,616/x
  3. Step 3: Cross multiply
    83,778x = 197,616 × 197,616
  4. Step 4: Simplify right side
    83,778x = 39,052,083,456
  5. Step 5: Solve for x
    x = 39,052,083,456/83,778
  6. Step 6: Final answer
    x = 466,137.69

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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.