Finding the Third Proportional to 2,538.50 and 3,699.75

Step by Step Solution

1. Step 1: Write the proportion equation
   2,538.50 : 3,699.75 = 3,699.75 : x
2. Step 2: Convert to fraction form
   2,538.50/3,699.75 = 3,699.75/x
3. Step 3: Cross multiply
   2,538.50x = 3,699.75 × 3,699.75
4. Step 4: Simplify right side
   2,538.50x = 13,688,150.06
5. Step 5: Solve for x
   x = 13,688,150.06/2,538.50
6. Step 6: Final answer
   x = 5,392.22