Finding the Third Proportional to 37,826 and 82,198

Step by Step Solution

1. Step 1: Write the proportion equation
   37,826 : 82,198 = 82,198 : x
2. Step 2: Convert to fraction form
   37,826/82,198 = 82,198/x
3. Step 3: Cross multiply
   37,826x = 82,198 × 82,198
4. Step 4: Simplify right side
   37,826x = 6,756,511,204
5. Step 5: Solve for x
   x = 6,756,511,204/37,826
6. Step 6: Final answer
   x = 178,620.82