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Finding the Third Proportional to 6,497 and 13,858

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Solution

The third proportional to 6,497 and 13,858 is: 29,558.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,497 : 13,858 = 13,858 : x
  2. Step 2: Convert to fraction form
    6,497/13,858 = 13,858/x
  3. Step 3: Cross multiply
    6,497x = 13,858 × 13,858
  4. Step 4: Simplify right side
    6,497x = 192,044,164
  5. Step 5: Solve for x
    x = 192,044,164/6,497
  6. Step 6: Final answer
    x = 29,558.90

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.