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Finding the Third Proportional to 5,982 and 12,782

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Solution

The third proportional to 5,982 and 12,782 is: 27,311.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,982 : 12,782 = 12,782 : x
  2. Step 2: Convert to fraction form
    5,982/12,782 = 12,782/x
  3. Step 3: Cross multiply
    5,982x = 12,782 × 12,782
  4. Step 4: Simplify right side
    5,982x = 163,379,524
  5. Step 5: Solve for x
    x = 163,379,524/5,982
  6. Step 6: Final answer
    x = 27,311.86

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.