Finding the Third Proportional to 11,616 and 16,384

Step by Step Solution

1. Step 1: Write the proportion equation
   11,616 : 16,384 = 16,384 : x
2. Step 2: Convert to fraction form
   11,616/16,384 = 16,384/x
3. Step 3: Cross multiply
   11,616x = 16,384 × 16,384
4. Step 4: Simplify right side
   11,616x = 268,435,456
5. Step 5: Solve for x
   x = 268,435,456/11,616
6. Step 6: Final answer
   x = 23,109.11