Finding the Third Proportional to 164 and 185.50

Step by Step Solution

1. Step 1: Write the proportion equation
   164 : 185.50 = 185.50 : x
2. Step 2: Convert to fraction form
   164/185.50 = 185.50/x
3. Step 3: Cross multiply
   164x = 185.50 × 185.50
4. Step 4: Simplify right side
   164x = 34,410.25
5. Step 5: Solve for x
   x = 34,410.25/164
6. Step 6: Final answer
   x = 209.82