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Finding the Third Proportional to 6,723 and 7,677

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Solution

The third proportional to 6,723 and 7,677 is: 8,766.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,723 : 7,677 = 7,677 : x
  2. Step 2: Convert to fraction form
    6,723/7,677 = 7,677/x
  3. Step 3: Cross multiply
    6,723x = 7,677 × 7,677
  4. Step 4: Simplify right side
    6,723x = 58,936,329
  5. Step 5: Solve for x
    x = 58,936,329/6,723
  6. Step 6: Final answer
    x = 8,766.37

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.