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Finding the Third Proportional to 2,569 and 5,993

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Solution

The third proportional to 2,569 and 5,993 is: 13,980.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,569 : 5,993 = 5,993 : x
  2. Step 2: Convert to fraction form
    2,569/5,993 = 5,993/x
  3. Step 3: Cross multiply
    2,569x = 5,993 × 5,993
  4. Step 4: Simplify right side
    2,569x = 35,916,049
  5. Step 5: Solve for x
    x = 35,916,049/2,569
  6. Step 6: Final answer
    x = 13,980.56

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.