Finding the Third Proportional to 82,980 and 178,824

Step by Step Solution

1. Step 1: Write the proportion equation
   82,980 : 178,824 = 178,824 : x
2. Step 2: Convert to fraction form
   82,980/178,824 = 178,824/x
3. Step 3: Cross multiply
   82,980x = 178,824 × 178,824
4. Step 4: Simplify right side
   82,980x = 31,978,022,976
5. Step 5: Solve for x
   x = 31,978,022,976/82,980
6. Step 6: Final answer
   x = 385,370.25