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Finding the Third Proportional to 414.75 and 564.75

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Solution

The third proportional to 414.75 and 564.75 is: 769.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.75 : 564.75 = 564.75 : x
  2. Step 2: Convert to fraction form
    414.75/564.75 = 564.75/x
  3. Step 3: Cross multiply
    414.75x = 564.75 × 564.75
  4. Step 4: Simplify right side
    414.75x = 318,942.56
  5. Step 5: Solve for x
    x = 318,942.56/414.75
  6. Step 6: Final answer
    x = 769.00

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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.