Finding the Third Proportional to 2,538 and 5,899.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538 : 5,899.50 = 5,899.50 : x
2. Step 2: Convert to fraction form
   2,538/5,899.50 = 5,899.50/x
3. Step 3: Cross multiply
   2,538x = 5,899.50 × 5,899.50
4. Step 4: Simplify right side
   2,538x = 34,804,100.25
5. Step 5: Solve for x
   x = 34,804,100.25/2,538
6. Step 6: Final answer
   x = 13,713.20