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Finding the Third Proportional to 381.38 and 420.56

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Solution

The third proportional to 381.38 and 420.56 is: 463.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    381.38 : 420.56 = 420.56 : x
  2. Step 2: Convert to fraction form
    381.38/420.56 = 420.56/x
  3. Step 3: Cross multiply
    381.38x = 420.56 × 420.56
  4. Step 4: Simplify right side
    381.38x = 176,872.82
  5. Step 5: Solve for x
    x = 176,872.82/381.38
  6. Step 6: Final answer
    x = 463.78

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.