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Finding the Third Proportional to 6,214 and 8,691

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Solution

The third proportional to 6,214 and 8,691 is: 12,155.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,214 : 8,691 = 8,691 : x
  2. Step 2: Convert to fraction form
    6,214/8,691 = 8,691/x
  3. Step 3: Cross multiply
    6,214x = 8,691 × 8,691
  4. Step 4: Simplify right side
    6,214x = 75,533,481
  5. Step 5: Solve for x
    x = 75,533,481/6,214
  6. Step 6: Final answer
    x = 12,155.37

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.