Finding the Third Proportional to 82,091 and 178,194

Step by Step Solution

1. Step 1: Write the proportion equation
   82,091 : 178,194 = 178,194 : x
2. Step 2: Convert to fraction form
   82,091/178,194 = 178,194/x
3. Step 3: Cross multiply
   82,091x = 178,194 × 178,194
4. Step 4: Simplify right side
   82,091x = 31,753,101,636
5. Step 5: Solve for x
   x = 31,753,101,636/82,091
6. Step 6: Final answer
   x = 386,803.69