Finding the Third Proportional to 82,678 and 178,451

Step by Step Solution

1. Step 1: Write the proportion equation
   82,678 : 178,451 = 178,451 : x
2. Step 2: Convert to fraction form
   82,678/178,451 = 178,451/x
3. Step 3: Cross multiply
   82,678x = 178,451 × 178,451
4. Step 4: Simplify right side
   82,678x = 31,844,759,401
5. Step 5: Solve for x
   x = 31,844,759,401/82,678
6. Step 6: Final answer
   x = 385,166.06