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Finding the Third Proportional to 1,198 and 1,906

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Solution

The third proportional to 1,198 and 1,906 is: 3,032.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,198 : 1,906 = 1,906 : x
  2. Step 2: Convert to fraction form
    1,198/1,906 = 1,906/x
  3. Step 3: Cross multiply
    1,198x = 1,906 × 1,906
  4. Step 4: Simplify right side
    1,198x = 3,632,836
  5. Step 5: Solve for x
    x = 3,632,836/1,198
  6. Step 6: Final answer
    x = 3,032.42

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.