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Finding the Third Proportional to 82,441 and 176,564

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Solution

The third proportional to 82,441 and 176,564 is: 378,147.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,441 : 176,564 = 176,564 : x
  2. Step 2: Convert to fraction form
    82,441/176,564 = 176,564/x
  3. Step 3: Cross multiply
    82,441x = 176,564 × 176,564
  4. Step 4: Simplify right side
    82,441x = 31,174,846,096
  5. Step 5: Solve for x
    x = 31,174,846,096/82,441
  6. Step 6: Final answer
    x = 378,147.36

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.