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Finding the Third Proportional to 37,842 and 82,234

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Solution

The third proportional to 37,842 and 82,234 is: 178,701.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,842 : 82,234 = 82,234 : x
  2. Step 2: Convert to fraction form
    37,842/82,234 = 82,234/x
  3. Step 3: Cross multiply
    37,842x = 82,234 × 82,234
  4. Step 4: Simplify right side
    37,842x = 6,762,430,756
  5. Step 5: Solve for x
    x = 6,762,430,756/37,842
  6. Step 6: Final answer
    x = 178,701.73

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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.