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Finding the Third Proportional to 257.91 and 414.42

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Solution

The third proportional to 257.91 and 414.42 is: 665.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.91 : 414.42 = 414.42 : x
  2. Step 2: Convert to fraction form
    257.91/414.42 = 414.42/x
  3. Step 3: Cross multiply
    257.91x = 414.42 × 414.42
  4. Step 4: Simplify right side
    257.91x = 171,745.49
  5. Step 5: Solve for x
    x = 171,745.49/257.91
  6. Step 6: Final answer
    x = 665.92

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.