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Finding the Third Proportional to 414.50 and 564.50

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Solution

The third proportional to 414.50 and 564.50 is: 768.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.50 : 564.50 = 564.50 : x
  2. Step 2: Convert to fraction form
    414.50/564.50 = 564.50/x
  3. Step 3: Cross multiply
    414.50x = 564.50 × 564.50
  4. Step 4: Simplify right side
    414.50x = 318,660.25
  5. Step 5: Solve for x
    x = 318,660.25/414.50
  6. Step 6: Final answer
    x = 768.78

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.