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Finding the Third Proportional to 405,934 and 642,743

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Solution

The third proportional to 405,934 and 642,743 is: 1,017,698.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    405,934 : 642,743 = 642,743 : x
  2. Step 2: Convert to fraction form
    405,934/642,743 = 642,743/x
  3. Step 3: Cross multiply
    405,934x = 642,743 × 642,743
  4. Step 4: Simplify right side
    405,934x = 413,118,564,049
  5. Step 5: Solve for x
    x = 413,118,564,049/405,934
  6. Step 6: Final answer
    x = 1,017,698.85

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.