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Finding the Third Proportional to 82,098 and 177,324

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Solution

The third proportional to 82,098 and 177,324 is: 383,003.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,098 : 177,324 = 177,324 : x
  2. Step 2: Convert to fraction form
    82,098/177,324 = 177,324/x
  3. Step 3: Cross multiply
    82,098x = 177,324 × 177,324
  4. Step 4: Simplify right side
    82,098x = 31,443,800,976
  5. Step 5: Solve for x
    x = 31,443,800,976/82,098
  6. Step 6: Final answer
    x = 383,003.25

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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.