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Finding the Third Proportional to 2,591 and 5,419

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Solution

The third proportional to 2,591 and 5,419 is: 11,333.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,591 : 5,419 = 5,419 : x
  2. Step 2: Convert to fraction form
    2,591/5,419 = 5,419/x
  3. Step 3: Cross multiply
    2,591x = 5,419 × 5,419
  4. Step 4: Simplify right side
    2,591x = 29,365,561
  5. Step 5: Solve for x
    x = 29,365,561/2,591
  6. Step 6: Final answer
    x = 11,333.68

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.