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Finding the Third Proportional to 37,787 and 82,198

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Solution

The third proportional to 37,787 and 82,198 is: 178,805.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,787 : 82,198 = 82,198 : x
  2. Step 2: Convert to fraction form
    37,787/82,198 = 82,198/x
  3. Step 3: Cross multiply
    37,787x = 82,198 × 82,198
  4. Step 4: Simplify right side
    37,787x = 6,756,511,204
  5. Step 5: Solve for x
    x = 6,756,511,204/37,787
  6. Step 6: Final answer
    x = 178,805.18

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.