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Finding the Third Proportional to 1,949 and 4,198

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Solution

The third proportional to 1,949 and 4,198 is: 9,042.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,949 : 4,198 = 4,198 : x
  2. Step 2: Convert to fraction form
    1,949/4,198 = 4,198/x
  3. Step 3: Cross multiply
    1,949x = 4,198 × 4,198
  4. Step 4: Simplify right side
    1,949x = 17,623,204
  5. Step 5: Solve for x
    x = 17,623,204/1,949
  6. Step 6: Final answer
    x = 9,042.18

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.