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Finding the Third Proportional to 197,834 and 419,210

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Solution

The third proportional to 197,834 and 419,210 is: 888,305.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,834 : 419,210 = 419,210 : x
  2. Step 2: Convert to fraction form
    197,834/419,210 = 419,210/x
  3. Step 3: Cross multiply
    197,834x = 419,210 × 419,210
  4. Step 4: Simplify right side
    197,834x = 175,737,024,100
  5. Step 5: Solve for x
    x = 175,737,024,100/197,834
  6. Step 6: Final answer
    x = 888,305.47

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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.