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Finding the Third Proportional to 41,077 and 84,097

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Solution

The third proportional to 41,077 and 84,097 is: 172,171.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    41,077 : 84,097 = 84,097 : x
  2. Step 2: Convert to fraction form
    41,077/84,097 = 84,097/x
  3. Step 3: Cross multiply
    41,077x = 84,097 × 84,097
  4. Step 4: Simplify right side
    41,077x = 7,072,305,409
  5. Step 5: Solve for x
    x = 7,072,305,409/41,077
  6. Step 6: Final answer
    x = 172,171.91

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.