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Finding the Third Proportional to 381.75 and 415.50

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Solution

The third proportional to 381.75 and 415.50 is: 452.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    381.75 : 415.50 = 415.50 : x
  2. Step 2: Convert to fraction form
    381.75/415.50 = 415.50/x
  3. Step 3: Cross multiply
    381.75x = 415.50 × 415.50
  4. Step 4: Simplify right side
    381.75x = 172,640.25
  5. Step 5: Solve for x
    x = 172,640.25/381.75
  6. Step 6: Final answer
    x = 452.23

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.