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Finding the Third Proportional to 2,002 and 3,698

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Solution

The third proportional to 2,002 and 3,698 is: 6,830.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,002 : 3,698 = 3,698 : x
  2. Step 2: Convert to fraction form
    2,002/3,698 = 3,698/x
  3. Step 3: Cross multiply
    2,002x = 3,698 × 3,698
  4. Step 4: Simplify right side
    2,002x = 13,675,204
  5. Step 5: Solve for x
    x = 13,675,204/2,002
  6. Step 6: Final answer
    x = 6,830.77

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.