Finding the Third Proportional to 16,384 and 17,824

Step by Step Solution

1. Step 1: Write the proportion equation
   16,384 : 17,824 = 17,824 : x
2. Step 2: Convert to fraction form
   16,384/17,824 = 17,824/x
3. Step 3: Cross multiply
   16,384x = 17,824 × 17,824
4. Step 4: Simplify right side
   16,384x = 317,694,976
5. Step 5: Solve for x
   x = 317,694,976/16,384
6. Step 6: Final answer
   x = 19,390.56