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Finding the Third Proportional to 82,214 and 176,905

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Solution

The third proportional to 82,214 and 176,905 is: 380,657.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,214 : 176,905 = 176,905 : x
  2. Step 2: Convert to fraction form
    82,214/176,905 = 176,905/x
  3. Step 3: Cross multiply
    82,214x = 176,905 × 176,905
  4. Step 4: Simplify right side
    82,214x = 31,295,379,025
  5. Step 5: Solve for x
    x = 31,295,379,025/82,214
  6. Step 6: Final answer
    x = 380,657.54

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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.