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Finding the Third Proportional to 825 and 1,831

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Solution

The third proportional to 825 and 1,831 is: 4,063.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    825 : 1,831 = 1,831 : x
  2. Step 2: Convert to fraction form
    825/1,831 = 1,831/x
  3. Step 3: Cross multiply
    825x = 1,831 × 1,831
  4. Step 4: Simplify right side
    825x = 3,352,561
  5. Step 5: Solve for x
    x = 3,352,561/825
  6. Step 6: Final answer
    x = 4,063.71

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.