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Finding the Third Proportional to 3,978 and 8,142

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Solution

The third proportional to 3,978 and 8,142 is: 16,664.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,978 : 8,142 = 8,142 : x
  2. Step 2: Convert to fraction form
    3,978/8,142 = 8,142/x
  3. Step 3: Cross multiply
    3,978x = 8,142 × 8,142
  4. Step 4: Simplify right side
    3,978x = 66,292,164
  5. Step 5: Solve for x
    x = 66,292,164/3,978
  6. Step 6: Final answer
    x = 16,664.70

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.