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Finding the Third Proportional to 400.13 and 523.31

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Solution

The third proportional to 400.13 and 523.31 is: 684.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    400.13 : 523.31 = 523.31 : x
  2. Step 2: Convert to fraction form
    400.13/523.31 = 523.31/x
  3. Step 3: Cross multiply
    400.13x = 523.31 × 523.31
  4. Step 4: Simplify right side
    400.13x = 273,855.97
  5. Step 5: Solve for x
    x = 273,855.97/400.13
  6. Step 6: Final answer
    x = 684.43

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.