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Finding the Third Proportional to 414.75 and 502.75

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Solution

The third proportional to 414.75 and 502.75 is: 609.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.75 : 502.75 = 502.75 : x
  2. Step 2: Convert to fraction form
    414.75/502.75 = 502.75/x
  3. Step 3: Cross multiply
    414.75x = 502.75 × 502.75
  4. Step 4: Simplify right side
    414.75x = 252,757.56
  5. Step 5: Solve for x
    x = 252,757.56/414.75
  6. Step 6: Final answer
    x = 609.42

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.