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Finding the Third Proportional to 49,701 and 106,419

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Solution

The third proportional to 49,701 and 106,419 is: 227,862.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,701 : 106,419 = 106,419 : x
  2. Step 2: Convert to fraction form
    49,701/106,419 = 106,419/x
  3. Step 3: Cross multiply
    49,701x = 106,419 × 106,419
  4. Step 4: Simplify right side
    49,701x = 11,325,003,561
  5. Step 5: Solve for x
    x = 11,325,003,561/49,701
  6. Step 6: Final answer
    x = 227,862.69

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.