Finding the Third Proportional to 105.25 and 164.75

Step by Step Solution

1. Step 1: Write the proportion equation
   105.25 : 164.75 = 164.75 : x
2. Step 2: Convert to fraction form
   105.25/164.75 = 164.75/x
3. Step 3: Cross multiply
   105.25x = 164.75 × 164.75
4. Step 4: Simplify right side
   105.25x = 27,142.56
5. Step 5: Solve for x
   x = 27,142.56/105.25
6. Step 6: Final answer
   x = 257.89