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Finding the Third Proportional to 682 and 749

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Solution

The third proportional to 682 and 749 is: 822.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    682 : 749 = 749 : x
  2. Step 2: Convert to fraction form
    682/749 = 749/x
  3. Step 3: Cross multiply
    682x = 749 × 749
  4. Step 4: Simplify right side
    682x = 561,001
  5. Step 5: Solve for x
    x = 561,001/682
  6. Step 6: Final answer
    x = 822.58

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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.