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Finding the Third Proportional to 5,409 and 11,638

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Solution

The third proportional to 5,409 and 11,638 is: 25,040.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,409 : 11,638 = 11,638 : x
  2. Step 2: Convert to fraction form
    5,409/11,638 = 11,638/x
  3. Step 3: Cross multiply
    5,409x = 11,638 × 11,638
  4. Step 4: Simplify right side
    5,409x = 135,443,044
  5. Step 5: Solve for x
    x = 135,443,044/5,409
  6. Step 6: Final answer
    x = 25,040.31

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.