Finding the Third Proportional to 138,024 and 195,729.75

Step by Step Solution

1. Step 1: Write the proportion equation
   138,024 : 195,729.75 = 195,729.75 : x
2. Step 2: Convert to fraction form
   138,024/195,729.75 = 195,729.75/x
3. Step 3: Cross multiply
   138,024x = 195,729.75 × 195,729.75
4. Step 4: Simplify right side
   138,024x = 38,310,135,035.06
5. Step 5: Solve for x
   x = 38,310,135,035.06/138,024
6. Step 6: Final answer
   x = 277,561.40