Finding the Third Proportional to 3,825 and 5,413.50

Step by Step Solution

1. Step 1: Write the proportion equation
   3,825 : 5,413.50 = 5,413.50 : x
2. Step 2: Convert to fraction form
   3,825/5,413.50 = 5,413.50/x
3. Step 3: Cross multiply
   3,825x = 5,413.50 × 5,413.50
4. Step 4: Simplify right side
   3,825x = 29,305,982.25
5. Step 5: Solve for x
   x = 29,305,982.25/3,825
6. Step 6: Final answer
   x = 7,661.69