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Finding the Third Proportional to 3,978 and 8,412

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Solution

The third proportional to 3,978 and 8,412 is: 17,788.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,978 : 8,412 = 8,412 : x
  2. Step 2: Convert to fraction form
    3,978/8,412 = 8,412/x
  3. Step 3: Cross multiply
    3,978x = 8,412 × 8,412
  4. Step 4: Simplify right side
    3,978x = 70,761,744
  5. Step 5: Solve for x
    x = 70,761,744/3,978
  6. Step 6: Final answer
    x = 17,788.27

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.