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Finding the Third Proportional to 38,097 and 82,170

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Solution

The third proportional to 38,097 and 82,170 is: 177,229.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,097 : 82,170 = 82,170 : x
  2. Step 2: Convert to fraction form
    38,097/82,170 = 82,170/x
  3. Step 3: Cross multiply
    38,097x = 82,170 × 82,170
  4. Step 4: Simplify right side
    38,097x = 6,751,908,900
  5. Step 5: Solve for x
    x = 6,751,908,900/38,097
  6. Step 6: Final answer
    x = 177,229.41

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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.