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Finding the Third Proportional to 397,408 and 597,741

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Solution

The third proportional to 397,408 and 597,741 is: 899,061.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    397,408 : 597,741 = 597,741 : x
  2. Step 2: Convert to fraction form
    397,408/597,741 = 597,741/x
  3. Step 3: Cross multiply
    397,408x = 597,741 × 597,741
  4. Step 4: Simplify right side
    397,408x = 357,294,303,081
  5. Step 5: Solve for x
    x = 357,294,303,081/397,408
  6. Step 6: Final answer
    x = 899,061.68

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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.