Finding the Third Proportional to 83 and 111

Step by Step Solution

1. Step 1: Write the proportion equation
   83 : 111 = 111 : x
2. Step 2: Convert to fraction form
   83/111 = 111/x
3. Step 3: Cross multiply
   83x = 111 × 111
4. Step 4: Simplify right side
   83x = 12,321
5. Step 5: Solve for x
   x = 12,321/83
6. Step 6: Final answer
   x = 148.45