Finding the Third Proportional to 1,538 and 3,597.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,538 : 3,597.50 = 3,597.50 : x
2. Step 2: Convert to fraction form
   1,538/3,597.50 = 3,597.50/x
3. Step 3: Cross multiply
   1,538x = 3,597.50 × 3,597.50
4. Step 4: Simplify right side
   1,538x = 12,942,006.25
5. Step 5: Solve for x
   x = 12,942,006.25/1,538
6. Step 6: Final answer
   x = 8,414.83