Finding the Third Proportional to 2,578 and 5,663

Step by Step Solution

1. Step 1: Write the proportion equation
   2,578 : 5,663 = 5,663 : x
2. Step 2: Convert to fraction form
   2,578/5,663 = 5,663/x
3. Step 3: Cross multiply
   2,578x = 5,663 × 5,663
4. Step 4: Simplify right side
   2,578x = 32,069,569
5. Step 5: Solve for x
   x = 32,069,569/2,578
6. Step 6: Final answer
   x = 12,439.71