Finding the Third Proportional to 82,438 and 178,016

Step by Step Solution

1. Step 1: Write the proportion equation
   82,438 : 178,016 = 178,016 : x
2. Step 2: Convert to fraction form
   82,438/178,016 = 178,016/x
3. Step 3: Cross multiply
   82,438x = 178,016 × 178,016
4. Step 4: Simplify right side
   82,438x = 31,689,696,256
5. Step 5: Solve for x
   x = 31,689,696,256/82,438
6. Step 6: Final answer
   x = 384,406.42