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Finding the Third Proportional to 409,589 and 614,384

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Solution

The third proportional to 409,589 and 614,384 is: 921,576.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    409,589 : 614,384 = 614,384 : x
  2. Step 2: Convert to fraction form
    409,589/614,384 = 614,384/x
  3. Step 3: Cross multiply
    409,589x = 614,384 × 614,384
  4. Step 4: Simplify right side
    409,589x = 377,467,699,456
  5. Step 5: Solve for x
    x = 377,467,699,456/409,589
  6. Step 6: Final answer
    x = 921,576.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.