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Finding the Third Proportional to 309,449 and 417,517

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Solution

The third proportional to 309,449 and 417,517 is: 563,325.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,449 : 417,517 = 417,517 : x
  2. Step 2: Convert to fraction form
    309,449/417,517 = 417,517/x
  3. Step 3: Cross multiply
    309,449x = 417,517 × 417,517
  4. Step 4: Simplify right side
    309,449x = 174,320,445,289
  5. Step 5: Solve for x
    x = 174,320,445,289/309,449
  6. Step 6: Final answer
    x = 563,325.28

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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.