Finding the Third Proportional to 96,680 and 214,096

Step by Step Solution

1. Step 1: Write the proportion equation
   96,680 : 214,096 = 214,096 : x
2. Step 2: Convert to fraction form
   96,680/214,096 = 214,096/x
3. Step 3: Cross multiply
   96,680x = 214,096 × 214,096
4. Step 4: Simplify right side
   96,680x = 45,837,097,216
5. Step 5: Solve for x
   x = 45,837,097,216/96,680
6. Step 6: Final answer
   x = 474,111.47