Finding the Third Proportional to 386.50 and 413.50

Step by Step Solution

1. Step 1: Write the proportion equation
   386.50 : 413.50 = 413.50 : x
2. Step 2: Convert to fraction form
   386.50/413.50 = 413.50/x
3. Step 3: Cross multiply
   386.50x = 413.50 × 413.50
4. Step 4: Simplify right side
   386.50x = 170,982.25
5. Step 5: Solve for x
   x = 170,982.25/386.50
6. Step 6: Final answer
   x = 442.39