Finding the Third Proportional to 82,686 and 178,464

Step by Step Solution

1. Step 1: Write the proportion equation
   82,686 : 178,464 = 178,464 : x
2. Step 2: Convert to fraction form
   82,686/178,464 = 178,464/x
3. Step 3: Cross multiply
   82,686x = 178,464 × 178,464
4. Step 4: Simplify right side
   82,686x = 31,849,399,296
5. Step 5: Solve for x
   x = 31,849,399,296/82,686
6. Step 6: Final answer
   x = 385,184.91