Finding the Third Proportional to 380 and 411.50

Step by Step Solution

1. Step 1: Write the proportion equation
   380 : 411.50 = 411.50 : x
2. Step 2: Convert to fraction form
   380/411.50 = 411.50/x
3. Step 3: Cross multiply
   380x = 411.50 × 411.50
4. Step 4: Simplify right side
   380x = 169,332.25
5. Step 5: Solve for x
   x = 169,332.25/380
6. Step 6: Final answer
   x = 445.61