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Finding the Third Proportional to 4,082 and 9,689

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Solution

The third proportional to 4,082 and 9,689 is: 22,997.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,082 : 9,689 = 9,689 : x
  2. Step 2: Convert to fraction form
    4,082/9,689 = 9,689/x
  3. Step 3: Cross multiply
    4,082x = 9,689 × 9,689
  4. Step 4: Simplify right side
    4,082x = 93,876,721
  5. Step 5: Solve for x
    x = 93,876,721/4,082
  6. Step 6: Final answer
    x = 22,997.73

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.