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Finding the Third Proportional to 397 and 809

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Solution

The third proportional to 397 and 809 is: 1,648.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    397 : 809 = 809 : x
  2. Step 2: Convert to fraction form
    397/809 = 809/x
  3. Step 3: Cross multiply
    397x = 809 × 809
  4. Step 4: Simplify right side
    397x = 654,481
  5. Step 5: Solve for x
    x = 654,481/397
  6. Step 6: Final answer
    x = 1,648.57

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.