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Finding the Third Proportional to 198,946 and 407,084

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Solution

The third proportional to 198,946 and 407,084 is: 832,976.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,946 : 407,084 = 407,084 : x
  2. Step 2: Convert to fraction form
    198,946/407,084 = 407,084/x
  3. Step 3: Cross multiply
    198,946x = 407,084 × 407,084
  4. Step 4: Simplify right side
    198,946x = 165,717,383,056
  5. Step 5: Solve for x
    x = 165,717,383,056/198,946
  6. Step 6: Final answer
    x = 832,976.70

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.