Finding the Third Proportional to 12.33 and 31.98

Step by Step Solution

1. Step 1: Write the proportion equation
   12.33 : 31.98 = 31.98 : x
2. Step 2: Convert to fraction form
   12.33/31.98 = 31.98/x
3. Step 3: Cross multiply
   12.33x = 31.98 × 31.98
4. Step 4: Simplify right side
   12.33x = 1,022.73
5. Step 5: Solve for x
   x = 1,022.73/12.33
6. Step 6: Final answer
   x = 82.95