Finding the Third Proportional to 32,768 and 71,085

Step by Step Solution

1. Step 1: Write the proportion equation
   32,768 : 71,085 = 71,085 : x
2. Step 2: Convert to fraction form
   32,768/71,085 = 71,085/x
3. Step 3: Cross multiply
   32,768x = 71,085 × 71,085
4. Step 4: Simplify right side
   32,768x = 5,053,077,225
5. Step 5: Solve for x
   x = 5,053,077,225/32,768
6. Step 6: Final answer
   x = 154,207.68