Finding the Third Proportional to 83,085 and 181,206

Step by Step Solution

1. Step 1: Write the proportion equation
   83,085 : 181,206 = 181,206 : x
2. Step 2: Convert to fraction form
   83,085/181,206 = 181,206/x
3. Step 3: Cross multiply
   83,085x = 181,206 × 181,206
4. Step 4: Simplify right side
   83,085x = 32,835,614,436
5. Step 5: Solve for x
   x = 32,835,614,436/83,085
6. Step 6: Final answer
   x = 395,205.08