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Finding the Third Proportional to 412 and 831

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Solution

The third proportional to 412 and 831 is: 1,676.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 831 = 831 : x
  2. Step 2: Convert to fraction form
    412/831 = 831/x
  3. Step 3: Cross multiply
    412x = 831 × 831
  4. Step 4: Simplify right side
    412x = 690,561
  5. Step 5: Solve for x
    x = 690,561/412
  6. Step 6: Final answer
    x = 1,676.12

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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.