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Finding the Third Proportional to 461,198 and 589,305

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Solution

The third proportional to 461,198 and 589,305 is: 752,996.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    461,198 : 589,305 = 589,305 : x
  2. Step 2: Convert to fraction form
    461,198/589,305 = 589,305/x
  3. Step 3: Cross multiply
    461,198x = 589,305 × 589,305
  4. Step 4: Simplify right side
    461,198x = 347,280,383,025
  5. Step 5: Solve for x
    x = 347,280,383,025/461,198
  6. Step 6: Final answer
    x = 752,996.29

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.