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Finding the Third Proportional to 411,914 and 619,977

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Solution

The third proportional to 411,914 and 619,977 is: 933,135.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    411,914 : 619,977 = 619,977 : x
  2. Step 2: Convert to fraction form
    411,914/619,977 = 619,977/x
  3. Step 3: Cross multiply
    411,914x = 619,977 × 619,977
  4. Step 4: Simplify right side
    411,914x = 384,371,480,529
  5. Step 5: Solve for x
    x = 384,371,480,529/411,914
  6. Step 6: Final answer
    x = 933,135.27

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.