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Finding the Third Proportional to 414,387 and 584,906

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Solution

The third proportional to 414,387 and 584,906 is: 825,593.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,387 : 584,906 = 584,906 : x
  2. Step 2: Convert to fraction form
    414,387/584,906 = 584,906/x
  3. Step 3: Cross multiply
    414,387x = 584,906 × 584,906
  4. Step 4: Simplify right side
    414,387x = 342,115,028,836
  5. Step 5: Solve for x
    x = 342,115,028,836/414,387
  6. Step 6: Final answer
    x = 825,593.05

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.