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Finding the Third Proportional to 414.66 and 563.44

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Solution

The third proportional to 414.66 and 563.44 is: 765.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.66 : 563.44 = 563.44 : x
  2. Step 2: Convert to fraction form
    414.66/563.44 = 563.44/x
  3. Step 3: Cross multiply
    414.66x = 563.44 × 563.44
  4. Step 4: Simplify right side
    414.66x = 317,461.82
  5. Step 5: Solve for x
    x = 317,461.82/414.66
  6. Step 6: Final answer
    x = 765.60

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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.