Finding the Third Proportional to 106.78 and 199.78

Step by Step Solution

1. Step 1: Write the proportion equation
   106.78 : 199.78 = 199.78 : x
2. Step 2: Convert to fraction form
   106.78/199.78 = 199.78/x
3. Step 3: Cross multiply
   106.78x = 199.78 × 199.78
4. Step 4: Simplify right side
   106.78x = 39,912.55
5. Step 5: Solve for x
   x = 39,912.55/106.78
6. Step 6: Final answer
   x = 373.78