Finding the Third Proportional to 82,784 and 178,796.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,784 : 178,796.50 = 178,796.50 : x
2. Step 2: Convert to fraction form
   82,784/178,796.50 = 178,796.50/x
3. Step 3: Cross multiply
   82,784x = 178,796.50 × 178,796.50
4. Step 4: Simplify right side
   82,784x = 31,968,188,412.25
5. Step 5: Solve for x
   x = 31,968,188,412.25/82,784
6. Step 6: Final answer
   x = 386,163.85