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Finding the Third Proportional to 81,972 and 177,876

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Solution

The third proportional to 81,972 and 177,876 is: 385,983.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,972 : 177,876 = 177,876 : x
  2. Step 2: Convert to fraction form
    81,972/177,876 = 177,876/x
  3. Step 3: Cross multiply
    81,972x = 177,876 × 177,876
  4. Step 4: Simplify right side
    81,972x = 31,639,871,376
  5. Step 5: Solve for x
    x = 31,639,871,376/81,972
  6. Step 6: Final answer
    x = 385,983.89

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.