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Finding the Third Proportional to 409 and 523

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Solution

The third proportional to 409 and 523 is: 668.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 523 = 523 : x
  2. Step 2: Convert to fraction form
    409/523 = 523/x
  3. Step 3: Cross multiply
    409x = 523 × 523
  4. Step 4: Simplify right side
    409x = 273,529
  5. Step 5: Solve for x
    x = 273,529/409
  6. Step 6: Final answer
    x = 668.78

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.