Finding the Third Proportional to 82,096 and 177,316

Step by Step Solution

1. Step 1: Write the proportion equation
   82,096 : 177,316 = 177,316 : x
2. Step 2: Convert to fraction form
   82,096/177,316 = 177,316/x
3. Step 3: Cross multiply
   82,096x = 177,316 × 177,316
4. Step 4: Simplify right side
   82,096x = 31,440,963,856
5. Step 5: Solve for x
   x = 31,440,963,856/82,096
6. Step 6: Final answer
   x = 382,978.02