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Finding the Third Proportional to 7,780 and 16,408

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Solution

The third proportional to 7,780 and 16,408 is: 34,604.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,780 : 16,408 = 16,408 : x
  2. Step 2: Convert to fraction form
    7,780/16,408 = 16,408/x
  3. Step 3: Cross multiply
    7,780x = 16,408 × 16,408
  4. Step 4: Simplify right side
    7,780x = 269,222,464
  5. Step 5: Solve for x
    x = 269,222,464/7,780
  6. Step 6: Final answer
    x = 34,604.43

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.