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Finding the Third Proportional to 42,098 and 97,469

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Solution

The third proportional to 42,098 and 97,469 is: 225,668.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,098 : 97,469 = 97,469 : x
  2. Step 2: Convert to fraction form
    42,098/97,469 = 97,469/x
  3. Step 3: Cross multiply
    42,098x = 97,469 × 97,469
  4. Step 4: Simplify right side
    42,098x = 9,500,205,961
  5. Step 5: Solve for x
    x = 9,500,205,961/42,098
  6. Step 6: Final answer
    x = 225,668.82

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.