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Finding the Third Proportional to 5,842 and 13,408

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Solution

The third proportional to 5,842 and 13,408 is: 30,772.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,842 : 13,408 = 13,408 : x
  2. Step 2: Convert to fraction form
    5,842/13,408 = 13,408/x
  3. Step 3: Cross multiply
    5,842x = 13,408 × 13,408
  4. Step 4: Simplify right side
    5,842x = 179,774,464
  5. Step 5: Solve for x
    x = 179,774,464/5,842
  6. Step 6: Final answer
    x = 30,772.76

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.