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Finding the Third Proportional to 419,648 and 665,512

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Solution

The third proportional to 419,648 and 665,512 is: 1,055,423.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,648 : 665,512 = 665,512 : x
  2. Step 2: Convert to fraction form
    419,648/665,512 = 665,512/x
  3. Step 3: Cross multiply
    419,648x = 665,512 × 665,512
  4. Step 4: Simplify right side
    419,648x = 442,906,222,144
  5. Step 5: Solve for x
    x = 442,906,222,144/419,648
  6. Step 6: Final answer
    x = 1,055,423.17

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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.