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Finding the Third Proportional to 419,642 and 665,503

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Solution

The third proportional to 419,642 and 665,503 is: 1,055,409.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,642 : 665,503 = 665,503 : x
  2. Step 2: Convert to fraction form
    419,642/665,503 = 665,503/x
  3. Step 3: Cross multiply
    419,642x = 665,503 × 665,503
  4. Step 4: Simplify right side
    419,642x = 442,894,243,009
  5. Step 5: Solve for x
    x = 442,894,243,009/419,642
  6. Step 6: Final answer
    x = 1,055,409.71

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.