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Finding the Third Proportional to 2,006 and 2,198

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Solution

The third proportional to 2,006 and 2,198 is: 2,408.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,006 : 2,198 = 2,198 : x
  2. Step 2: Convert to fraction form
    2,006/2,198 = 2,198/x
  3. Step 3: Cross multiply
    2,006x = 2,198 × 2,198
  4. Step 4: Simplify right side
    2,006x = 4,831,204
  5. Step 5: Solve for x
    x = 4,831,204/2,006
  6. Step 6: Final answer
    x = 2,408.38

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.