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Finding the Third Proportional to 381.75 and 469.25

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Solution

The third proportional to 381.75 and 469.25 is: 576.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    381.75 : 469.25 = 469.25 : x
  2. Step 2: Convert to fraction form
    381.75/469.25 = 469.25/x
  3. Step 3: Cross multiply
    381.75x = 469.25 × 469.25
  4. Step 4: Simplify right side
    381.75x = 220,195.56
  5. Step 5: Solve for x
    x = 220,195.56/381.75
  6. Step 6: Final answer
    x = 576.81

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.