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Finding the Third Proportional to 2,296 and 5,198

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Solution

The third proportional to 2,296 and 5,198 is: 11,767.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,296 : 5,198 = 5,198 : x
  2. Step 2: Convert to fraction form
    2,296/5,198 = 5,198/x
  3. Step 3: Cross multiply
    2,296x = 5,198 × 5,198
  4. Step 4: Simplify right side
    2,296x = 27,019,204
  5. Step 5: Solve for x
    x = 27,019,204/2,296
  6. Step 6: Final answer
    x = 11,767.95

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Why These Related Problems?

These problems maintain the same ratio (2.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.