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Finding the Third Proportional to 37,821 and 82,567

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Solution

The third proportional to 37,821 and 82,567 is: 180,251.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,821 : 82,567 = 82,567 : x
  2. Step 2: Convert to fraction form
    37,821/82,567 = 82,567/x
  3. Step 3: Cross multiply
    37,821x = 82,567 × 82,567
  4. Step 4: Simplify right side
    37,821x = 6,817,309,489
  5. Step 5: Solve for x
    x = 6,817,309,489/37,821
  6. Step 6: Final answer
    x = 180,251.96

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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.