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Finding the Third Proportional to 82,164 and 176,782

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Solution

The third proportional to 82,164 and 176,782 is: 380,359.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,164 : 176,782 = 176,782 : x
  2. Step 2: Convert to fraction form
    82,164/176,782 = 176,782/x
  3. Step 3: Cross multiply
    82,164x = 176,782 × 176,782
  4. Step 4: Simplify right side
    82,164x = 31,251,875,524
  5. Step 5: Solve for x
    x = 31,251,875,524/82,164
  6. Step 6: Final answer
    x = 380,359.71

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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.