Finding the Third Proportional to 82,584 and 181,208

Step by Step Solution

1. Step 1: Write the proportion equation
   82,584 : 181,208 = 181,208 : x
2. Step 2: Convert to fraction form
   82,584/181,208 = 181,208/x
3. Step 3: Cross multiply
   82,584x = 181,208 × 181,208
4. Step 4: Simplify right side
   82,584x = 32,836,339,264
5. Step 5: Solve for x
   x = 32,836,339,264/82,584
6. Step 6: Final answer
   x = 397,611.39