Finding the Third Proportional to 511.50 and 765.38

Step by Step Solution

1. Step 1: Write the proportion equation
   511.50 : 765.38 = 765.38 : x
2. Step 2: Convert to fraction form
   511.50/765.38 = 765.38/x
3. Step 3: Cross multiply
   511.50x = 765.38 × 765.38
4. Step 4: Simplify right side
   511.50x = 585,798.89
5. Step 5: Solve for x
   x = 585,798.89/511.50
6. Step 6: Final answer
   x = 1,145.26