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Finding the Third Proportional to 10,406 and 15,957

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Solution

The third proportional to 10,406 and 15,957 is: 24,469.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,406 : 15,957 = 15,957 : x
  2. Step 2: Convert to fraction form
    10,406/15,957 = 15,957/x
  3. Step 3: Cross multiply
    10,406x = 15,957 × 15,957
  4. Step 4: Simplify right side
    10,406x = 254,625,849
  5. Step 5: Solve for x
    x = 254,625,849/10,406
  6. Step 6: Final answer
    x = 24,469.14

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.