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Finding the Third Proportional to 814 and 1,234

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Solution

The third proportional to 814 and 1,234 is: 1,870.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    814 : 1,234 = 1,234 : x
  2. Step 2: Convert to fraction form
    814/1,234 = 1,234/x
  3. Step 3: Cross multiply
    814x = 1,234 × 1,234
  4. Step 4: Simplify right side
    814x = 1,522,756
  5. Step 5: Solve for x
    x = 1,522,756/814
  6. Step 6: Final answer
    x = 1,870.71

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.