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Finding the Third Proportional to 37,976 and 83,227

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Solution

The third proportional to 37,976 and 83,227 is: 182,397.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,976 : 83,227 = 83,227 : x
  2. Step 2: Convert to fraction form
    37,976/83,227 = 83,227/x
  3. Step 3: Cross multiply
    37,976x = 83,227 × 83,227
  4. Step 4: Simplify right side
    37,976x = 6,926,733,529
  5. Step 5: Solve for x
    x = 6,926,733,529/37,976
  6. Step 6: Final answer
    x = 182,397.66

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.