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Finding the Third Proportional to 83,221 and 178,106

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Solution

The third proportional to 83,221 and 178,106 is: 381,174.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,221 : 178,106 = 178,106 : x
  2. Step 2: Convert to fraction form
    83,221/178,106 = 178,106/x
  3. Step 3: Cross multiply
    83,221x = 178,106 × 178,106
  4. Step 4: Simplify right side
    83,221x = 31,721,747,236
  5. Step 5: Solve for x
    x = 31,721,747,236/83,221
  6. Step 6: Final answer
    x = 381,174.79

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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.