Finding the Third Proportional to 120,902 and 177,665

Step by Step Solution

1. Step 1: Write the proportion equation
   120,902 : 177,665 = 177,665 : x
2. Step 2: Convert to fraction form
   120,902/177,665 = 177,665/x
3. Step 3: Cross multiply
   120,902x = 177,665 × 177,665
4. Step 4: Simplify right side
   120,902x = 31,564,852,225
5. Step 5: Solve for x
   x = 31,564,852,225/120,902
6. Step 6: Final answer
   x = 261,078.00