Finding the Fourth Proportional to 105.86, 146.22 and 85.16

Step by Step Solution

1. Step 1: Write the proportion equation
   105.86 : 146.22 = 85.16 : x
2. Step 2: Convert to fraction form
   105.86/146.22 = 85.16/x
3. Step 3: Cross multiply
   105.86x = 146.22 × 85.16
4. Step 4: Simplify right side
   105.86x = 12,452.10
5. Step 5: Solve for x
   x = 12,452.10/105.86
6. Step 6: Final answer
   x = 117.63