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Finding the Third Proportional to 13,831 and 20,782

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Solution

The third proportional to 13,831 and 20,782 is: 31,226.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,831 : 20,782 = 20,782 : x
  2. Step 2: Convert to fraction form
    13,831/20,782 = 20,782/x
  3. Step 3: Cross multiply
    13,831x = 20,782 × 20,782
  4. Step 4: Simplify right side
    13,831x = 431,891,524
  5. Step 5: Solve for x
    x = 431,891,524/13,831
  6. Step 6: Final answer
    x = 31,226.34

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.