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Finding the Third Proportional to 414,392 and 584,913

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Solution

The third proportional to 414,392 and 584,913 is: 825,602.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,392 : 584,913 = 584,913 : x
  2. Step 2: Convert to fraction form
    414,392/584,913 = 584,913/x
  3. Step 3: Cross multiply
    414,392x = 584,913 × 584,913
  4. Step 4: Simplify right side
    414,392x = 342,123,217,569
  5. Step 5: Solve for x
    x = 342,123,217,569/414,392
  6. Step 6: Final answer
    x = 825,602.85

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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.