Finding the Third Proportional to 82,128 and 176,824

Step by Step Solution

1. Step 1: Write the proportion equation
   82,128 : 176,824 = 176,824 : x
2. Step 2: Convert to fraction form
   82,128/176,824 = 176,824/x
3. Step 3: Cross multiply
   82,128x = 176,824 × 176,824
4. Step 4: Simplify right side
   82,128x = 31,266,726,976
5. Step 5: Solve for x
   x = 31,266,726,976/82,128
6. Step 6: Final answer
   x = 380,707.27