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Finding the Third Proportional to 614 and 1,589

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Solution

The third proportional to 614 and 1,589 is: 4,112.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    614 : 1,589 = 1,589 : x
  2. Step 2: Convert to fraction form
    614/1,589 = 1,589/x
  3. Step 3: Cross multiply
    614x = 1,589 × 1,589
  4. Step 4: Simplify right side
    614x = 2,524,921
  5. Step 5: Solve for x
    x = 2,524,921/614
  6. Step 6: Final answer
    x = 4,112.25

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Why These Related Problems?

These problems maintain the same ratio (2.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.