Finding the Third Proportional to 2,585 and 5,578.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,585 : 5,578.50 = 5,578.50 : x
2. Step 2: Convert to fraction form
   2,585/5,578.50 = 5,578.50/x
3. Step 3: Cross multiply
   2,585x = 5,578.50 × 5,578.50
4. Step 4: Simplify right side
   2,585x = 31,119,662.25
5. Step 5: Solve for x
   x = 31,119,662.25/2,585
6. Step 6: Final answer
   x = 12,038.55