Finding the Third Proportional to 2,586 and 5,661

Step by Step Solution

1. Step 1: Write the proportion equation
   2,586 : 5,661 = 5,661 : x
2. Step 2: Convert to fraction form
   2,586/5,661 = 5,661/x
3. Step 3: Cross multiply
   2,586x = 5,661 × 5,661
4. Step 4: Simplify right side
   2,586x = 32,046,921
5. Step 5: Solve for x
   x = 32,046,921/2,586
6. Step 6: Final answer
   x = 12,392.47