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Finding the Third Proportional to 49,408 and 106,538

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Solution

The third proportional to 49,408 and 106,538 is: 229,726.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,408 : 106,538 = 106,538 : x
  2. Step 2: Convert to fraction form
    49,408/106,538 = 106,538/x
  3. Step 3: Cross multiply
    49,408x = 106,538 × 106,538
  4. Step 4: Simplify right side
    49,408x = 11,350,345,444
  5. Step 5: Solve for x
    x = 11,350,345,444/49,408
  6. Step 6: Final answer
    x = 229,726.88

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.