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Finding the Third Proportional to 82,237 and 177,165

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Solution

The third proportional to 82,237 and 177,165 is: 381,670.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,237 : 177,165 = 177,165 : x
  2. Step 2: Convert to fraction form
    82,237/177,165 = 177,165/x
  3. Step 3: Cross multiply
    82,237x = 177,165 × 177,165
  4. Step 4: Simplify right side
    82,237x = 31,387,437,225
  5. Step 5: Solve for x
    x = 31,387,437,225/82,237
  6. Step 6: Final answer
    x = 381,670.50

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.