Finding the Third Proportional to 82,780 and 178,792.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,780 : 178,792.50 = 178,792.50 : x
2. Step 2: Convert to fraction form
   82,780/178,792.50 = 178,792.50/x
3. Step 3: Cross multiply
   82,780x = 178,792.50 × 178,792.50
4. Step 4: Simplify right side
   82,780x = 31,966,758,056.25
5. Step 5: Solve for x
   x = 31,966,758,056.25/82,780
6. Step 6: Final answer
   x = 386,165.23