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Finding the Third Proportional to 83,114 and 178,135

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Solution

The third proportional to 83,114 and 178,135 is: 381,789.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,114 : 178,135 = 178,135 : x
  2. Step 2: Convert to fraction form
    83,114/178,135 = 178,135/x
  3. Step 3: Cross multiply
    83,114x = 178,135 × 178,135
  4. Step 4: Simplify right side
    83,114x = 31,732,078,225
  5. Step 5: Solve for x
    x = 31,732,078,225/83,114
  6. Step 6: Final answer
    x = 381,789.81

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.