Finding the Third Proportional to 82,838 and 178,792

Step by Step Solution

1. Step 1: Write the proportion equation
   82,838 : 178,792 = 178,792 : x
2. Step 2: Convert to fraction form
   82,838/178,792 = 178,792/x
3. Step 3: Cross multiply
   82,838x = 178,792 × 178,792
4. Step 4: Simplify right side
   82,838x = 31,966,579,264
5. Step 5: Solve for x
   x = 31,966,579,264/82,838
6. Step 6: Final answer
   x = 385,892.70