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Finding the Third Proportional to 81,971 and 178,156

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Solution

The third proportional to 81,971 and 178,156 is: 387,204.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,971 : 178,156 = 178,156 : x
  2. Step 2: Convert to fraction form
    81,971/178,156 = 178,156/x
  3. Step 3: Cross multiply
    81,971x = 178,156 × 178,156
  4. Step 4: Simplify right side
    81,971x = 31,739,560,336
  5. Step 5: Solve for x
    x = 31,739,560,336/81,971
  6. Step 6: Final answer
    x = 387,204.75

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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.