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Finding the Third Proportional to 199,001 and 409,682

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Solution

The third proportional to 199,001 and 409,682 is: 843,409.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    199,001 : 409,682 = 409,682 : x
  2. Step 2: Convert to fraction form
    199,001/409,682 = 409,682/x
  3. Step 3: Cross multiply
    199,001x = 409,682 × 409,682
  4. Step 4: Simplify right side
    199,001x = 167,839,341,124
  5. Step 5: Solve for x
    x = 167,839,341,124/199,001
  6. Step 6: Final answer
    x = 843,409.54

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.