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Finding the Third Proportional to 9,682 and 22,415

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Solution

The third proportional to 9,682 and 22,415 is: 51,893.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,682 : 22,415 = 22,415 : x
  2. Step 2: Convert to fraction form
    9,682/22,415 = 22,415/x
  3. Step 3: Cross multiply
    9,682x = 22,415 × 22,415
  4. Step 4: Simplify right side
    9,682x = 502,432,225
  5. Step 5: Solve for x
    x = 502,432,225/9,682
  6. Step 6: Final answer
    x = 51,893.43

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.