Finding the Third Proportional to 1,686 and 2,413.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,686 : 2,413.50 = 2,413.50 : x
2. Step 2: Convert to fraction form
   1,686/2,413.50 = 2,413.50/x
3. Step 3: Cross multiply
   1,686x = 2,413.50 × 2,413.50
4. Step 4: Simplify right side
   1,686x = 5,824,982.25
5. Step 5: Solve for x
   x = 5,824,982.25/1,686
6. Step 6: Final answer
   x = 3,454.91