Finding the Third Proportional to 82,194 and 177,238

Step by Step Solution

1. Step 1: Write the proportion equation
   82,194 : 177,238 = 177,238 : x
2. Step 2: Convert to fraction form
   82,194/177,238 = 177,238/x
3. Step 3: Cross multiply
   82,194x = 177,238 × 177,238
4. Step 4: Simplify right side
   82,194x = 31,413,308,644
5. Step 5: Solve for x
   x = 31,413,308,644/82,194
6. Step 6: Final answer
   x = 382,184.94