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Finding the Third Proportional to 2,138 and 4,186

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Solution

The third proportional to 2,138 and 4,186 is: 8,195.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,138 : 4,186 = 4,186 : x
  2. Step 2: Convert to fraction form
    2,138/4,186 = 4,186/x
  3. Step 3: Cross multiply
    2,138x = 4,186 × 4,186
  4. Step 4: Simplify right side
    2,138x = 17,522,596
  5. Step 5: Solve for x
    x = 17,522,596/2,138
  6. Step 6: Final answer
    x = 8,195.79

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.