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Finding the Third Proportional to 81,977 and 122,966

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Solution

The third proportional to 81,977 and 122,966 is: 184,449.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,977 : 122,966 = 122,966 : x
  2. Step 2: Convert to fraction form
    81,977/122,966 = 122,966/x
  3. Step 3: Cross multiply
    81,977x = 122,966 × 122,966
  4. Step 4: Simplify right side
    81,977x = 15,120,637,156
  5. Step 5: Solve for x
    x = 15,120,637,156/81,977
  6. Step 6: Final answer
    x = 184,449.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.