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Finding the Third Proportional to 2,137 and 4,663

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Solution

The third proportional to 2,137 and 4,663 is: 10,174.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,137 : 4,663 = 4,663 : x
  2. Step 2: Convert to fraction form
    2,137/4,663 = 4,663/x
  3. Step 3: Cross multiply
    2,137x = 4,663 × 4,663
  4. Step 4: Simplify right side
    2,137x = 21,743,569
  5. Step 5: Solve for x
    x = 21,743,569/2,137
  6. Step 6: Final answer
    x = 10,174.81

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.