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Finding the Third Proportional to 49,734 and 106,830

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Solution

The third proportional to 49,734 and 106,830 is: 229,473.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,734 : 106,830 = 106,830 : x
  2. Step 2: Convert to fraction form
    49,734/106,830 = 106,830/x
  3. Step 3: Cross multiply
    49,734x = 106,830 × 106,830
  4. Step 4: Simplify right side
    49,734x = 11,412,648,900
  5. Step 5: Solve for x
    x = 11,412,648,900/49,734
  6. Step 6: Final answer
    x = 229,473.78

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.