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Finding the Third Proportional to 414.28 and 580.73

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Solution

The third proportional to 414.28 and 580.73 is: 814.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.28 : 580.73 = 580.73 : x
  2. Step 2: Convert to fraction form
    414.28/580.73 = 580.73/x
  3. Step 3: Cross multiply
    414.28x = 580.73 × 580.73
  4. Step 4: Simplify right side
    414.28x = 337,252.41
  5. Step 5: Solve for x
    x = 337,252.41/414.28
  6. Step 6: Final answer
    x = 814.07

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.