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Finding the Third Proportional to 2,098 and 3,198

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Solution

The third proportional to 2,098 and 3,198 is: 4,874.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,098 : 3,198 = 3,198 : x
  2. Step 2: Convert to fraction form
    2,098/3,198 = 3,198/x
  3. Step 3: Cross multiply
    2,098x = 3,198 × 3,198
  4. Step 4: Simplify right side
    2,098x = 10,227,204
  5. Step 5: Solve for x
    x = 10,227,204/2,098
  6. Step 6: Final answer
    x = 4,874.74

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.