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Finding the Third Proportional to 37,854 and 82,341

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Solution

The third proportional to 37,854 and 82,341 is: 179,110.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,854 : 82,341 = 82,341 : x
  2. Step 2: Convert to fraction form
    37,854/82,341 = 82,341/x
  3. Step 3: Cross multiply
    37,854x = 82,341 × 82,341
  4. Step 4: Simplify right side
    37,854x = 6,780,040,281
  5. Step 5: Solve for x
    x = 6,780,040,281/37,854
  6. Step 6: Final answer
    x = 179,110.27

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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.