Finding the Third Proportional to 33,538 and 82,854

Step by Step Solution

1. Step 1: Write the proportion equation
   33,538 : 82,854 = 82,854 : x
2. Step 2: Convert to fraction form
   33,538/82,854 = 82,854/x
3. Step 3: Cross multiply
   33,538x = 82,854 × 82,854
4. Step 4: Simplify right side
   33,538x = 6,864,785,316
5. Step 5: Solve for x
   x = 6,864,785,316/33,538
6. Step 6: Final answer
   x = 204,686.78