Finding the Third Proportional to 685 and 1,038.50

Step by Step Solution

1. Step 1: Write the proportion equation
   685 : 1,038.50 = 1,038.50 : x
2. Step 2: Convert to fraction form
   685/1,038.50 = 1,038.50/x
3. Step 3: Cross multiply
   685x = 1,038.50 × 1,038.50
4. Step 4: Simplify right side
   685x = 1,078,482.25
5. Step 5: Solve for x
   x = 1,078,482.25/685
6. Step 6: Final answer
   x = 1,574.43