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Finding the Third Proportional to 3,680 and 8,212

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Solution

The third proportional to 3,680 and 8,212 is: 18,325.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,680 : 8,212 = 8,212 : x
  2. Step 2: Convert to fraction form
    3,680/8,212 = 8,212/x
  3. Step 3: Cross multiply
    3,680x = 8,212 × 8,212
  4. Step 4: Simplify right side
    3,680x = 67,436,944
  5. Step 5: Solve for x
    x = 67,436,944/3,680
  6. Step 6: Final answer
    x = 18,325.26

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.