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Finding the Third Proportional to 38,041 and 82,097

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Solution

The third proportional to 38,041 and 82,097 is: 177,175.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,041 : 82,097 = 82,097 : x
  2. Step 2: Convert to fraction form
    38,041/82,097 = 82,097/x
  3. Step 3: Cross multiply
    38,041x = 82,097 × 82,097
  4. Step 4: Simplify right side
    38,041x = 6,739,917,409
  5. Step 5: Solve for x
    x = 6,739,917,409/38,041
  6. Step 6: Final answer
    x = 177,175.09

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.