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Finding the Third Proportional to 419 and 823

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Solution

The third proportional to 419 and 823 is: 1,616.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    419 : 823 = 823 : x
  2. Step 2: Convert to fraction form
    419/823 = 823/x
  3. Step 3: Cross multiply
    419x = 823 × 823
  4. Step 4: Simplify right side
    419x = 677,329
  5. Step 5: Solve for x
    x = 677,329/419
  6. Step 6: Final answer
    x = 1,616.54

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Why These Related Problems?

These problems maintain the same ratio (1.96) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.