Finding the Third Proportional to 105,777 and 165,096.75

Step by Step Solution

1. Step 1: Write the proportion equation
   105,777 : 165,096.75 = 165,096.75 : x
2. Step 2: Convert to fraction form
   105,777/165,096.75 = 165,096.75/x
3. Step 3: Cross multiply
   105,777x = 165,096.75 × 165,096.75
4. Step 4: Simplify right side
   105,777x = 27,256,936,860.56
5. Step 5: Solve for x
   x = 27,256,936,860.56/105,777
6. Step 6: Final answer
   x = 257,683.02