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Finding the Third Proportional to 234 and 406

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Solution

The third proportional to 234 and 406 is: 704.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    234 : 406 = 406 : x
  2. Step 2: Convert to fraction form
    234/406 = 406/x
  3. Step 3: Cross multiply
    234x = 406 × 406
  4. Step 4: Simplify right side
    234x = 164,836
  5. Step 5: Solve for x
    x = 164,836/234
  6. Step 6: Final answer
    x = 704.43

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Why These Related Problems?

These problems maintain the same ratio (1.74) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.