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Finding the Third Proportional to 82,006 and 177,614

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Solution

The third proportional to 82,006 and 177,614 is: 384,688.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,006 : 177,614 = 177,614 : x
  2. Step 2: Convert to fraction form
    82,006/177,614 = 177,614/x
  3. Step 3: Cross multiply
    82,006x = 177,614 × 177,614
  4. Step 4: Simplify right side
    82,006x = 31,546,732,996
  5. Step 5: Solve for x
    x = 31,546,732,996/82,006
  6. Step 6: Final answer
    x = 384,688.11

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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.