Finding the Third Proportional to 82,016 and 173,824

Step by Step Solution

1. Step 1: Write the proportion equation
   82,016 : 173,824 = 173,824 : x
2. Step 2: Convert to fraction form
   82,016/173,824 = 173,824/x
3. Step 3: Cross multiply
   82,016x = 173,824 × 173,824
4. Step 4: Simplify right side
   82,016x = 30,214,782,976
5. Step 5: Solve for x
   x = 30,214,782,976/82,016
6. Step 6: Final answer
   x = 368,401.08