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Finding the Third Proportional to 2,000 and 4,100

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Solution

The third proportional to 2,000 and 4,100 is: 8,405

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,000 : 4,100 = 4,100 : x
  2. Step 2: Convert to fraction form
    2,000/4,100 = 4,100/x
  3. Step 3: Cross multiply
    2,000x = 4,100 × 4,100
  4. Step 4: Simplify right side
    2,000x = 16,810,000
  5. Step 5: Solve for x
    x = 16,810,000/2,000
  6. Step 6: Final answer
    x = 8,405

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.