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Finding the Third Proportional to 6,401 and 8,649

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Solution

The third proportional to 6,401 and 8,649 is: 11,686.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,401 : 8,649 = 8,649 : x
  2. Step 2: Convert to fraction form
    6,401/8,649 = 8,649/x
  3. Step 3: Cross multiply
    6,401x = 8,649 × 8,649
  4. Step 4: Simplify right side
    6,401x = 74,805,201
  5. Step 5: Solve for x
    x = 74,805,201/6,401
  6. Step 6: Final answer
    x = 11,686.49

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.