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Finding the Third Proportional to 6,814 and 9,665

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Solution

The third proportional to 6,814 and 9,665 is: 13,708.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,814 : 9,665 = 9,665 : x
  2. Step 2: Convert to fraction form
    6,814/9,665 = 9,665/x
  3. Step 3: Cross multiply
    6,814x = 9,665 × 9,665
  4. Step 4: Simplify right side
    6,814x = 93,412,225
  5. Step 5: Solve for x
    x = 93,412,225/6,814
  6. Step 6: Final answer
    x = 13,708.87

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.