Finding the Third Proportional to 117,546 and 177,411.75

Step by Step Solution

1. Step 1: Write the proportion equation
   117,546 : 177,411.75 = 177,411.75 : x
2. Step 2: Convert to fraction form
   117,546/177,411.75 = 177,411.75/x
3. Step 3: Cross multiply
   117,546x = 177,411.75 × 177,411.75
4. Step 4: Simplify right side
   117,546x = 31,474,929,038.06
5. Step 5: Solve for x
   x = 31,474,929,038.06/117,546
6. Step 6: Final answer
   x = 267,766.91