Finding the Third Proportional to 685.50 and 829.50

Step by Step Solution

1. Step 1: Write the proportion equation
   685.50 : 829.50 = 829.50 : x
2. Step 2: Convert to fraction form
   685.50/829.50 = 829.50/x
3. Step 3: Cross multiply
   685.50x = 829.50 × 829.50
4. Step 4: Simplify right side
   685.50x = 688,070.25
5. Step 5: Solve for x
   x = 688,070.25/685.50
6. Step 6: Final answer
   x = 1,003.75