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Finding the Third Proportional to 6,586 and 8,002

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Solution

The third proportional to 6,586 and 8,002 is: 9,722.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,586 : 8,002 = 8,002 : x
  2. Step 2: Convert to fraction form
    6,586/8,002 = 8,002/x
  3. Step 3: Cross multiply
    6,586x = 8,002 × 8,002
  4. Step 4: Simplify right side
    6,586x = 64,032,004
  5. Step 5: Solve for x
    x = 64,032,004/6,586
  6. Step 6: Final answer
    x = 9,722.44

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.