Finding the Third Proportional to 382.22 and 413.86

Step by Step Solution

1. Step 1: Write the proportion equation
   382.22 : 413.86 = 413.86 : x
2. Step 2: Convert to fraction form
   382.22/413.86 = 413.86/x
3. Step 3: Cross multiply
   382.22x = 413.86 × 413.86
4. Step 4: Simplify right side
   382.22x = 171,279.58
5. Step 5: Solve for x
   x = 171,279.58/382.22
6. Step 6: Final answer
   x = 448.12