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Finding the Third Proportional to 13,814 and 21,542

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Solution

The third proportional to 13,814 and 21,542 is: 33,593.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,814 : 21,542 = 21,542 : x
  2. Step 2: Convert to fraction form
    13,814/21,542 = 21,542/x
  3. Step 3: Cross multiply
    13,814x = 21,542 × 21,542
  4. Step 4: Simplify right side
    13,814x = 464,057,764
  5. Step 5: Solve for x
    x = 464,057,764/13,814
  6. Step 6: Final answer
    x = 33,593.29

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.