Finding the Third Proportional to 2,601 and 5,642

Step by Step Solution

1. Step 1: Write the proportion equation
   2,601 : 5,642 = 5,642 : x
2. Step 2: Convert to fraction form
   2,601/5,642 = 5,642/x
3. Step 3: Cross multiply
   2,601x = 5,642 × 5,642
4. Step 4: Simplify right side
   2,601x = 31,832,164
5. Step 5: Solve for x
   x = 31,832,164/2,601
6. Step 6: Final answer
   x = 12,238.43