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Finding the Third Proportional to 82,181 and 177,346

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Solution

The third proportional to 82,181 and 177,346 is: 382,711.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,181 : 177,346 = 177,346 : x
  2. Step 2: Convert to fraction form
    82,181/177,346 = 177,346/x
  3. Step 3: Cross multiply
    82,181x = 177,346 × 177,346
  4. Step 4: Simplify right side
    82,181x = 31,451,603,716
  5. Step 5: Solve for x
    x = 31,451,603,716/82,181
  6. Step 6: Final answer
    x = 382,711.38

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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.