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Finding the Third Proportional to 7,677 and 16,122

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Solution

The third proportional to 7,677 and 16,122 is: 33,856.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,677 : 16,122 = 16,122 : x
  2. Step 2: Convert to fraction form
    7,677/16,122 = 16,122/x
  3. Step 3: Cross multiply
    7,677x = 16,122 × 16,122
  4. Step 4: Simplify right side
    7,677x = 259,918,884
  5. Step 5: Solve for x
    x = 259,918,884/7,677
  6. Step 6: Final answer
    x = 33,856.83

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.