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Finding the Third Proportional to 5,978 and 8,206

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Solution

The third proportional to 5,978 and 8,206 is: 11,264.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,978 : 8,206 = 8,206 : x
  2. Step 2: Convert to fraction form
    5,978/8,206 = 8,206/x
  3. Step 3: Cross multiply
    5,978x = 8,206 × 8,206
  4. Step 4: Simplify right side
    5,978x = 67,338,436
  5. Step 5: Solve for x
    x = 67,338,436/5,978
  6. Step 6: Final answer
    x = 11,264.38

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.