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Finding the Third Proportional to 2,069 and 4,084

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Solution

The third proportional to 2,069 and 4,084 is: 8,061.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,069 : 4,084 = 4,084 : x
  2. Step 2: Convert to fraction form
    2,069/4,084 = 4,084/x
  3. Step 3: Cross multiply
    2,069x = 4,084 × 4,084
  4. Step 4: Simplify right side
    2,069x = 16,679,056
  5. Step 5: Solve for x
    x = 16,679,056/2,069
  6. Step 6: Final answer
    x = 8,061.41

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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.