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Finding the Third Proportional to 269,972 and 419,107

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Solution

The third proportional to 269,972 and 419,107 is: 650,625.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    269,972 : 419,107 = 419,107 : x
  2. Step 2: Convert to fraction form
    269,972/419,107 = 419,107/x
  3. Step 3: Cross multiply
    269,972x = 419,107 × 419,107
  4. Step 4: Simplify right side
    269,972x = 175,650,677,449
  5. Step 5: Solve for x
    x = 175,650,677,449/269,972
  6. Step 6: Final answer
    x = 650,625.54

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.