Finding the Third Proportional to 31.78 and 83.06

Step by Step Solution

1. Step 1: Write the proportion equation
   31.78 : 83.06 = 83.06 : x
2. Step 2: Convert to fraction form
   31.78/83.06 = 83.06/x
3. Step 3: Cross multiply
   31.78x = 83.06 × 83.06
4. Step 4: Simplify right side
   31.78x = 6,899.38
5. Step 5: Solve for x
   x = 6,899.38/31.78
6. Step 6: Final answer
   x = 217.09