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Finding the Third Proportional to 197,831 and 419,206

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Solution

The third proportional to 197,831 and 419,206 is: 888,301.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,831 : 419,206 = 419,206 : x
  2. Step 2: Convert to fraction form
    197,831/419,206 = 419,206/x
  3. Step 3: Cross multiply
    197,831x = 419,206 × 419,206
  4. Step 4: Simplify right side
    197,831x = 175,733,670,436
  5. Step 5: Solve for x
    x = 175,733,670,436/197,831
  6. Step 6: Final answer
    x = 888,301.99

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.