Finding the Third Proportional to 82,311 and 177,105

Step by Step Solution

1. Step 1: Write the proportion equation
   82,311 : 177,105 = 177,105 : x
2. Step 2: Convert to fraction form
   82,311/177,105 = 177,105/x
3. Step 3: Cross multiply
   82,311x = 177,105 × 177,105
4. Step 4: Simplify right side
   82,311x = 31,366,181,025
5. Step 5: Solve for x
   x = 31,366,181,025/82,311
6. Step 6: Final answer
   x = 381,069.13