Finding the Third Proportional to 82,256 and 178,606

Step by Step Solution

1. Step 1: Write the proportion equation
   82,256 : 178,606 = 178,606 : x
2. Step 2: Convert to fraction form
   82,256/178,606 = 178,606/x
3. Step 3: Cross multiply
   82,256x = 178,606 × 178,606
4. Step 4: Simplify right side
   82,256x = 31,900,103,236
5. Step 5: Solve for x
   x = 31,900,103,236/82,256
6. Step 6: Final answer
   x = 387,814.91