Finding the Third Proportional to 105.25 and 164.50

Step by Step Solution

1. Step 1: Write the proportion equation
   105.25 : 164.50 = 164.50 : x
2. Step 2: Convert to fraction form
   105.25/164.50 = 164.50/x
3. Step 3: Cross multiply
   105.25x = 164.50 × 164.50
4. Step 4: Simplify right side
   105.25x = 27,060.25
5. Step 5: Solve for x
   x = 27,060.25/105.25
6. Step 6: Final answer
   x = 257.10