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Finding the Third Proportional to 205.38 and 284.69

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Solution

The third proportional to 205.38 and 284.69 is: 394.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.38 : 284.69 = 284.69 : x
  2. Step 2: Convert to fraction form
    205.38/284.69 = 284.69/x
  3. Step 3: Cross multiply
    205.38x = 284.69 × 284.69
  4. Step 4: Simplify right side
    205.38x = 81,046.97
  5. Step 5: Solve for x
    x = 81,046.97/205.38
  6. Step 6: Final answer
    x = 394.63

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Why These Related Problems?

These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.