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Finding the Third Proportional to 82,371 and 177,567

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Solution

The third proportional to 82,371 and 177,567 is: 382,780.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,371 : 177,567 = 177,567 : x
  2. Step 2: Convert to fraction form
    82,371/177,567 = 177,567/x
  3. Step 3: Cross multiply
    82,371x = 177,567 × 177,567
  4. Step 4: Simplify right side
    82,371x = 31,530,039,489
  5. Step 5: Solve for x
    x = 31,530,039,489/82,371
  6. Step 6: Final answer
    x = 382,780.83

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.