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Finding the Third Proportional to 10,406 and 22,663

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Solution

The third proportional to 10,406 and 22,663 is: 49,357.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,406 : 22,663 = 22,663 : x
  2. Step 2: Convert to fraction form
    10,406/22,663 = 22,663/x
  3. Step 3: Cross multiply
    10,406x = 22,663 × 22,663
  4. Step 4: Simplify right side
    10,406x = 513,611,569
  5. Step 5: Solve for x
    x = 513,611,569/10,406
  6. Step 6: Final answer
    x = 49,357.25

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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.