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Finding the Third Proportional to 6,414 and 13,722

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Solution

The third proportional to 6,414 and 13,722 is: 29,356.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,414 : 13,722 = 13,722 : x
  2. Step 2: Convert to fraction form
    6,414/13,722 = 13,722/x
  3. Step 3: Cross multiply
    6,414x = 13,722 × 13,722
  4. Step 4: Simplify right side
    6,414x = 188,293,284
  5. Step 5: Solve for x
    x = 188,293,284/6,414
  6. Step 6: Final answer
    x = 29,356.61

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.