Finding the Third Proportional to 82,406 and 177,610

Step by Step Solution

1. Step 1: Write the proportion equation
   82,406 : 177,610 = 177,610 : x
2. Step 2: Convert to fraction form
   82,406/177,610 = 177,610/x
3. Step 3: Cross multiply
   82,406x = 177,610 × 177,610
4. Step 4: Simplify right side
   82,406x = 31,545,312,100
5. Step 5: Solve for x
   x = 31,545,312,100/82,406
6. Step 6: Final answer
   x = 382,803.58