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Finding the Third Proportional to 9,689 and 20,523

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Solution

The third proportional to 9,689 and 20,523 is: 43,471.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,689 : 20,523 = 20,523 : x
  2. Step 2: Convert to fraction form
    9,689/20,523 = 20,523/x
  3. Step 3: Cross multiply
    9,689x = 20,523 × 20,523
  4. Step 4: Simplify right side
    9,689x = 421,193,529
  5. Step 5: Solve for x
    x = 421,193,529/9,689
  6. Step 6: Final answer
    x = 43,471.31

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.