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Finding the Third Proportional to 408 and 823

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Solution

The third proportional to 408 and 823 is: 1,660.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    408 : 823 = 823 : x
  2. Step 2: Convert to fraction form
    408/823 = 823/x
  3. Step 3: Cross multiply
    408x = 823 × 823
  4. Step 4: Simplify right side
    408x = 677,329
  5. Step 5: Solve for x
    x = 677,329/408
  6. Step 6: Final answer
    x = 1,660.12

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.