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Finding the Third Proportional to 7,692 and 16,408

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Solution

The third proportional to 7,692 and 16,408 is: 35,000.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,692 : 16,408 = 16,408 : x
  2. Step 2: Convert to fraction form
    7,692/16,408 = 16,408/x
  3. Step 3: Cross multiply
    7,692x = 16,408 × 16,408
  4. Step 4: Simplify right side
    7,692x = 269,222,464
  5. Step 5: Solve for x
    x = 269,222,464/7,692
  6. Step 6: Final answer
    x = 35,000.32

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.