Finding the Third Proportional to 16,384 and 35,543

Step by Step Solution

1. Step 1: Write the proportion equation
   16,384 : 35,543 = 35,543 : x
2. Step 2: Convert to fraction form
   16,384/35,543 = 35,543/x
3. Step 3: Cross multiply
   16,384x = 35,543 × 35,543
4. Step 4: Simplify right side
   16,384x = 1,263,304,849
5. Step 5: Solve for x
   x = 1,263,304,849/16,384
6. Step 6: Final answer
   x = 77,106.01