Finding the Third Proportional to 82,692 and 178,264

Step by Step Solution

1. Step 1: Write the proportion equation
   82,692 : 178,264 = 178,264 : x
2. Step 2: Convert to fraction form
   82,692/178,264 = 178,264/x
3. Step 3: Cross multiply
   82,692x = 178,264 × 178,264
4. Step 4: Simplify right side
   82,692x = 31,778,053,696
5. Step 5: Solve for x
   x = 31,778,053,696/82,692
6. Step 6: Final answer
   x = 384,294.17