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Finding the Third Proportional to 205.78 and 424.78

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Solution

The third proportional to 205.78 and 424.78 is: 876.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    205.78 : 424.78 = 424.78 : x
  2. Step 2: Convert to fraction form
    205.78/424.78 = 424.78/x
  3. Step 3: Cross multiply
    205.78x = 424.78 × 424.78
  4. Step 4: Simplify right side
    205.78x = 180,439.11
  5. Step 5: Solve for x
    x = 180,439.11/205.78
  6. Step 6: Final answer
    x = 876.85

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.