Finding the Third Proportional to 82,684 and 178,462

Step by Step Solution

1. Step 1: Write the proportion equation
   82,684 : 178,462 = 178,462 : x
2. Step 2: Convert to fraction form
   82,684/178,462 = 178,462/x
3. Step 3: Cross multiply
   82,684x = 178,462 × 178,462
4. Step 4: Simplify right side
   82,684x = 31,848,685,444
5. Step 5: Solve for x
   x = 31,848,685,444/82,684
6. Step 6: Final answer
   x = 385,185.59