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Finding the Third Proportional to 272,325 and 419,971

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Solution

The third proportional to 272,325 and 419,971 is: 647,665.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    272,325 : 419,971 = 419,971 : x
  2. Step 2: Convert to fraction form
    272,325/419,971 = 419,971/x
  3. Step 3: Cross multiply
    272,325x = 419,971 × 419,971
  4. Step 4: Simplify right side
    272,325x = 176,375,640,841
  5. Step 5: Solve for x
    x = 176,375,640,841/272,325
  6. Step 6: Final answer
    x = 647,665.99

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.