Finding the Third Proportional to 416.50 and 765.50

Step by Step Solution

1. Step 1: Write the proportion equation
   416.50 : 765.50 = 765.50 : x
2. Step 2: Convert to fraction form
   416.50/765.50 = 765.50/x
3. Step 3: Cross multiply
   416.50x = 765.50 × 765.50
4. Step 4: Simplify right side
   416.50x = 585,990.25
5. Step 5: Solve for x
   x = 585,990.25/416.50
6. Step 6: Final answer
   x = 1,406.94