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Finding the Third Proportional to 402,430 and 563,997

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Solution

The third proportional to 402,430 and 563,997 is: 790,429.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    402,430 : 563,997 = 563,997 : x
  2. Step 2: Convert to fraction form
    402,430/563,997 = 563,997/x
  3. Step 3: Cross multiply
    402,430x = 563,997 × 563,997
  4. Step 4: Simplify right side
    402,430x = 318,092,616,009
  5. Step 5: Solve for x
    x = 318,092,616,009/402,430
  6. Step 6: Final answer
    x = 790,429.68

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.