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Finding the Third Proportional to 82,182 and 177,477

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Solution

The third proportional to 82,182 and 177,477 is: 383,272.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,182 : 177,477 = 177,477 : x
  2. Step 2: Convert to fraction form
    82,182/177,477 = 177,477/x
  3. Step 3: Cross multiply
    82,182x = 177,477 × 177,477
  4. Step 4: Simplify right side
    82,182x = 31,498,085,529
  5. Step 5: Solve for x
    x = 31,498,085,529/82,182
  6. Step 6: Final answer
    x = 383,272.32

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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.