Finding the Third Proportional to 2,578.50 and 3,642.75

Step by Step Solution

1. Step 1: Write the proportion equation
   2,578.50 : 3,642.75 = 3,642.75 : x
2. Step 2: Convert to fraction form
   2,578.50/3,642.75 = 3,642.75/x
3. Step 3: Cross multiply
   2,578.50x = 3,642.75 × 3,642.75
4. Step 4: Simplify right side
   2,578.50x = 13,269,627.56
5. Step 5: Solve for x
   x = 13,269,627.56/2,578.50
6. Step 6: Final answer
   x = 5,146.26