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Finding the Third Proportional to 38,204 and 82,051

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Solution

The third proportional to 38,204 and 82,051 is: 176,221.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,204 : 82,051 = 82,051 : x
  2. Step 2: Convert to fraction form
    38,204/82,051 = 82,051/x
  3. Step 3: Cross multiply
    38,204x = 82,051 × 82,051
  4. Step 4: Simplify right side
    38,204x = 6,732,366,601
  5. Step 5: Solve for x
    x = 6,732,366,601/38,204
  6. Step 6: Final answer
    x = 176,221.51

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.