Finding the Third Proportional to 8,096 and 17,578

Step by Step Solution

1. Step 1: Write the proportion equation
   8,096 : 17,578 = 17,578 : x
2. Step 2: Convert to fraction form
   8,096/17,578 = 17,578/x
3. Step 3: Cross multiply
   8,096x = 17,578 × 17,578
4. Step 4: Simplify right side
   8,096x = 308,986,084
5. Step 5: Solve for x
   x = 308,986,084/8,096
6. Step 6: Final answer
   x = 38,165.28