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Finding the Third Proportional to 414,394 and 584,916

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Solution

The third proportional to 414,394 and 584,916 is: 825,607.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,394 : 584,916 = 584,916 : x
  2. Step 2: Convert to fraction form
    414,394/584,916 = 584,916/x
  3. Step 3: Cross multiply
    414,394x = 584,916 × 584,916
  4. Step 4: Simplify right side
    414,394x = 342,126,727,056
  5. Step 5: Solve for x
    x = 342,126,727,056/414,394
  6. Step 6: Final answer
    x = 825,607.34

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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.