Finding the Third Proportional to 105.38 and 166.50

Step by Step Solution

1. Step 1: Write the proportion equation
   105.38 : 166.50 = 166.50 : x
2. Step 2: Convert to fraction form
   105.38/166.50 = 166.50/x
3. Step 3: Cross multiply
   105.38x = 166.50 × 166.50
4. Step 4: Simplify right side
   105.38x = 27,722.25
5. Step 5: Solve for x
   x = 27,722.25/105.38
6. Step 6: Final answer
   x = 263.08