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Finding the Third Proportional to 384.75 and 414.38

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Solution

The third proportional to 384.75 and 414.38 is: 446.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    384.75 : 414.38 = 414.38 : x
  2. Step 2: Convert to fraction form
    384.75/414.38 = 414.38/x
  3. Step 3: Cross multiply
    384.75x = 414.38 × 414.38
  4. Step 4: Simplify right side
    384.75x = 171,706.64
  5. Step 5: Solve for x
    x = 171,706.64/384.75
  6. Step 6: Final answer
    x = 446.28

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.