Finding the Third Proportional to 83,022 and 178,138

Step by Step Solution

1. Step 1: Write the proportion equation
   83,022 : 178,138 = 178,138 : x
2. Step 2: Convert to fraction form
   83,022/178,138 = 178,138/x
3. Step 3: Cross multiply
   83,022x = 178,138 × 178,138
4. Step 4: Simplify right side
   83,022x = 31,733,147,044
5. Step 5: Solve for x
   x = 31,733,147,044/83,022
6. Step 6: Final answer
   x = 382,225.76