Finding the Third Proportional to 2,585 and 5,578

Step by Step Solution

1. Step 1: Write the proportion equation
   2,585 : 5,578 = 5,578 : x
2. Step 2: Convert to fraction form
   2,585/5,578 = 5,578/x
3. Step 3: Cross multiply
   2,585x = 5,578 × 5,578
4. Step 4: Simplify right side
   2,585x = 31,114,084
5. Step 5: Solve for x
   x = 31,114,084/2,585
6. Step 6: Final answer
   x = 12,036.40