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Finding the Third Proportional to 309,098 and 417,963

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Solution

The third proportional to 309,098 and 417,963 is: 565,170.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,098 : 417,963 = 417,963 : x
  2. Step 2: Convert to fraction form
    309,098/417,963 = 417,963/x
  3. Step 3: Cross multiply
    309,098x = 417,963 × 417,963
  4. Step 4: Simplify right side
    309,098x = 174,693,069,369
  5. Step 5: Solve for x
    x = 174,693,069,369/309,098
  6. Step 6: Final answer
    x = 565,170.49

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.