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Finding the Third Proportional to 77,978 and 164,104

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Solution

The third proportional to 77,978 and 164,104 is: 345,355.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,978 : 164,104 = 164,104 : x
  2. Step 2: Convert to fraction form
    77,978/164,104 = 164,104/x
  3. Step 3: Cross multiply
    77,978x = 164,104 × 164,104
  4. Step 4: Simplify right side
    77,978x = 26,930,122,816
  5. Step 5: Solve for x
    x = 26,930,122,816/77,978
  6. Step 6: Final answer
    x = 345,355.39

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.