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Finding the Third Proportional to 412,914 and 581,451

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Solution

The third proportional to 412,914 and 581,451 is: 818,778.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,914 : 581,451 = 581,451 : x
  2. Step 2: Convert to fraction form
    412,914/581,451 = 581,451/x
  3. Step 3: Cross multiply
    412,914x = 581,451 × 581,451
  4. Step 4: Simplify right side
    412,914x = 338,085,265,401
  5. Step 5: Solve for x
    x = 338,085,265,401/412,914
  6. Step 6: Final answer
    x = 818,778.89

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.