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Finding the Third Proportional to 6,829 and 9,661

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Solution

The third proportional to 6,829 and 9,661 is: 13,667.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,829 : 9,661 = 9,661 : x
  2. Step 2: Convert to fraction form
    6,829/9,661 = 9,661/x
  3. Step 3: Cross multiply
    6,829x = 9,661 × 9,661
  4. Step 4: Simplify right side
    6,829x = 93,334,921
  5. Step 5: Solve for x
    x = 93,334,921/6,829
  6. Step 6: Final answer
    x = 13,667.44

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.