Finding the Third Proportional to 82,824 and 178,762

Step by Step Solution

1. Step 1: Write the proportion equation
   82,824 : 178,762 = 178,762 : x
2. Step 2: Convert to fraction form
   82,824/178,762 = 178,762/x
3. Step 3: Cross multiply
   82,824x = 178,762 × 178,762
4. Step 4: Simplify right side
   82,824x = 31,955,852,644
5. Step 5: Solve for x
   x = 31,955,852,644/82,824
6. Step 6: Final answer
   x = 385,828.42