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Finding the Third Proportional to 83,108 and 197,564

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Solution

The third proportional to 83,108 and 197,564 is: 469,648.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,108 : 197,564 = 197,564 : x
  2. Step 2: Convert to fraction form
    83,108/197,564 = 197,564/x
  3. Step 3: Cross multiply
    83,108x = 197,564 × 197,564
  4. Step 4: Simplify right side
    83,108x = 39,031,534,096
  5. Step 5: Solve for x
    x = 39,031,534,096/83,108
  6. Step 6: Final answer
    x = 469,648.34

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.