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Finding the Third Proportional to 838 and 1,198

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Solution

The third proportional to 838 and 1,198 is: 1,712.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    838 : 1,198 = 1,198 : x
  2. Step 2: Convert to fraction form
    838/1,198 = 1,198/x
  3. Step 3: Cross multiply
    838x = 1,198 × 1,198
  4. Step 4: Simplify right side
    838x = 1,435,204
  5. Step 5: Solve for x
    x = 1,435,204/838
  6. Step 6: Final answer
    x = 1,712.65

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.