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Finding the Third Proportional to 997 and 2,041

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Solution

The third proportional to 997 and 2,041 is: 4,178.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    997 : 2,041 = 2,041 : x
  2. Step 2: Convert to fraction form
    997/2,041 = 2,041/x
  3. Step 3: Cross multiply
    997x = 2,041 × 2,041
  4. Step 4: Simplify right side
    997x = 4,165,681
  5. Step 5: Solve for x
    x = 4,165,681/997
  6. Step 6: Final answer
    x = 4,178.22

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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.