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Finding the Third Proportional to 269,739 and 419,097

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Solution

The third proportional to 269,739 and 419,097 is: 651,156.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    269,739 : 419,097 = 419,097 : x
  2. Step 2: Convert to fraction form
    269,739/419,097 = 419,097/x
  3. Step 3: Cross multiply
    269,739x = 419,097 × 419,097
  4. Step 4: Simplify right side
    269,739x = 175,642,295,409
  5. Step 5: Solve for x
    x = 175,642,295,409/269,739
  6. Step 6: Final answer
    x = 651,156.47

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.