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Finding the Third Proportional to 382.13 and 415.31

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Solution

The third proportional to 382.13 and 415.31 is: 451.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    382.13 : 415.31 = 415.31 : x
  2. Step 2: Convert to fraction form
    382.13/415.31 = 415.31/x
  3. Step 3: Cross multiply
    382.13x = 415.31 × 415.31
  4. Step 4: Simplify right side
    382.13x = 172,484.47
  5. Step 5: Solve for x
    x = 172,484.47/382.13
  6. Step 6: Final answer
    x = 451.38

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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.