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Finding the Third Proportional to 5,200 and 8,589

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Solution

The third proportional to 5,200 and 8,589 is: 14,186.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,200 : 8,589 = 8,589 : x
  2. Step 2: Convert to fraction form
    5,200/8,589 = 8,589/x
  3. Step 3: Cross multiply
    5,200x = 8,589 × 8,589
  4. Step 4: Simplify right side
    5,200x = 73,770,921
  5. Step 5: Solve for x
    x = 73,770,921/5,200
  6. Step 6: Final answer
    x = 14,186.72

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.