Finding the Third Proportional to 766.50 and 1,782

Step by Step Solution

1. Step 1: Write the proportion equation
   766.50 : 1,782 = 1,782 : x
2. Step 2: Convert to fraction form
   766.50/1,782 = 1,782/x
3. Step 3: Cross multiply
   766.50x = 1,782 × 1,782
4. Step 4: Simplify right side
   766.50x = 3,175,524
5. Step 5: Solve for x
   x = 3,175,524/766.50
6. Step 6: Final answer
   x = 4,142.89