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Finding the Third Proportional to 272,306 and 419,941

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Solution

The third proportional to 272,306 and 419,941 is: 647,618.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    272,306 : 419,941 = 419,941 : x
  2. Step 2: Convert to fraction form
    272,306/419,941 = 419,941/x
  3. Step 3: Cross multiply
    272,306x = 419,941 × 419,941
  4. Step 4: Simplify right side
    272,306x = 176,350,443,481
  5. Step 5: Solve for x
    x = 176,350,443,481/272,306
  6. Step 6: Final answer
    x = 647,618.65

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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.