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Finding the Third Proportional to 697 and 771

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Solution

The third proportional to 697 and 771 is: 852.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    697 : 771 = 771 : x
  2. Step 2: Convert to fraction form
    697/771 = 771/x
  3. Step 3: Cross multiply
    697x = 771 × 771
  4. Step 4: Simplify right side
    697x = 594,441
  5. Step 5: Solve for x
    x = 594,441/697
  6. Step 6: Final answer
    x = 852.86

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.