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Finding the Third Proportional to 82,414 and 180,866

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Solution

The third proportional to 82,414 and 180,866 is: 396,929.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,414 : 180,866 = 180,866 : x
  2. Step 2: Convert to fraction form
    82,414/180,866 = 180,866/x
  3. Step 3: Cross multiply
    82,414x = 180,866 × 180,866
  4. Step 4: Simplify right side
    82,414x = 32,712,509,956
  5. Step 5: Solve for x
    x = 32,712,509,956/82,414
  6. Step 6: Final answer
    x = 396,929.04

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.