Finding the Third Proportional to 2,538 and 3,796.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 3,796.50 = 3,796.50 : x
2. Step 2: Convert to fraction form
   2,538/3,796.50 = 3,796.50/x
3. Step 3: Cross multiply
   2,538x = 3,796.50 × 3,796.50
4. Step 4: Simplify right side
   2,538x = 14,413,412.25
5. Step 5: Solve for x
   x = 14,413,412.25/2,538
6. Step 6: Final answer
   x = 5,679.04