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Finding the Third Proportional to 419,037 and 648,711

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Solution

The third proportional to 419,037 and 648,711 is: 1,004,269.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,037 : 648,711 = 648,711 : x
  2. Step 2: Convert to fraction form
    419,037/648,711 = 648,711/x
  3. Step 3: Cross multiply
    419,037x = 648,711 × 648,711
  4. Step 4: Simplify right side
    419,037x = 420,825,961,521
  5. Step 5: Solve for x
    x = 420,825,961,521/419,037
  6. Step 6: Final answer
    x = 1,004,269.22

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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.