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Finding the Third Proportional to 2,109 and 4,165

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Solution

The third proportional to 2,109 and 4,165 is: 8,225.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,109 : 4,165 = 4,165 : x
  2. Step 2: Convert to fraction form
    2,109/4,165 = 4,165/x
  3. Step 3: Cross multiply
    2,109x = 4,165 × 4,165
  4. Step 4: Simplify right side
    2,109x = 17,347,225
  5. Step 5: Solve for x
    x = 17,347,225/2,109
  6. Step 6: Final answer
    x = 8,225.33

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Why These Related Problems?

These problems maintain the same ratio (1.97) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.