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Finding the Third Proportional to 37,827 and 82,206

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Solution

The third proportional to 37,827 and 82,206 is: 178,650.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,827 : 82,206 = 82,206 : x
  2. Step 2: Convert to fraction form
    37,827/82,206 = 82,206/x
  3. Step 3: Cross multiply
    37,827x = 82,206 × 82,206
  4. Step 4: Simplify right side
    37,827x = 6,757,826,436
  5. Step 5: Solve for x
    x = 6,757,826,436/37,827
  6. Step 6: Final answer
    x = 178,650.87

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.