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Finding the Third Proportional to 37,838 and 82,226

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Solution

The third proportional to 37,838 and 82,226 is: 178,685.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,838 : 82,226 = 82,226 : x
  2. Step 2: Convert to fraction form
    37,838/82,226 = 82,226/x
  3. Step 3: Cross multiply
    37,838x = 82,226 × 82,226
  4. Step 4: Simplify right side
    37,838x = 6,761,115,076
  5. Step 5: Solve for x
    x = 6,761,115,076/37,838
  6. Step 6: Final answer
    x = 178,685.85

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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.