Finding the Third Proportional to 82,641 and 178,399.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,641 : 178,399.50 = 178,399.50 : x
2. Step 2: Convert to fraction form
   82,641/178,399.50 = 178,399.50/x
3. Step 3: Cross multiply
   82,641x = 178,399.50 × 178,399.50
4. Step 4: Simplify right side
   82,641x = 31,826,381,600.25
5. Step 5: Solve for x
   x = 31,826,381,600.25/82,641
6. Step 6: Final answer
   x = 385,116.12