Finding the Third Proportional to 256 and 401.50

Step by Step Solution

1. Step 1: Write the proportion equation
   256 : 401.50 = 401.50 : x
2. Step 2: Convert to fraction form
   256/401.50 = 401.50/x
3. Step 3: Cross multiply
   256x = 401.50 × 401.50
4. Step 4: Simplify right side
   256x = 161,202.25
5. Step 5: Solve for x
   x = 161,202.25/256
6. Step 6: Final answer
   x = 629.70