Finding the Third Proportional to 82,688 and 178,256

Step by Step Solution

1. Step 1: Write the proportion equation
   82,688 : 178,256 = 178,256 : x
2. Step 2: Convert to fraction form
   82,688/178,256 = 178,256/x
3. Step 3: Cross multiply
   82,688x = 178,256 × 178,256
4. Step 4: Simplify right side
   82,688x = 31,775,201,536
5. Step 5: Solve for x
   x = 31,775,201,536/82,688
6. Step 6: Final answer
   x = 384,278.27