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Finding the Third Proportional to 49,970 and 106,414

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Solution

The third proportional to 49,970 and 106,414 is: 226,614.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,970 : 106,414 = 106,414 : x
  2. Step 2: Convert to fraction form
    49,970/106,414 = 106,414/x
  3. Step 3: Cross multiply
    49,970x = 106,414 × 106,414
  4. Step 4: Simplify right side
    49,970x = 11,323,939,396
  5. Step 5: Solve for x
    x = 11,323,939,396/49,970
  6. Step 6: Final answer
    x = 226,614.76

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.