Finding the Third Proportional to 768 and 1,411.50

Step by Step Solution

1. Step 1: Write the proportion equation
   768 : 1,411.50 = 1,411.50 : x
2. Step 2: Convert to fraction form
   768/1,411.50 = 1,411.50/x
3. Step 3: Cross multiply
   768x = 1,411.50 × 1,411.50
4. Step 4: Simplify right side
   768x = 1,992,332.25
5. Step 5: Solve for x
   x = 1,992,332.25/768
6. Step 6: Final answer
   x = 2,594.18