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Finding the Third Proportional to 198,942 and 407,077

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Solution

The third proportional to 198,942 and 407,077 is: 832,964.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,942 : 407,077 = 407,077 : x
  2. Step 2: Convert to fraction form
    198,942/407,077 = 407,077/x
  3. Step 3: Cross multiply
    198,942x = 407,077 × 407,077
  4. Step 4: Simplify right side
    198,942x = 165,711,683,929
  5. Step 5: Solve for x
    x = 165,711,683,929/198,942
  6. Step 6: Final answer
    x = 832,964.80

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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.