Finding the Third Proportional to 516.56 and 766.69

Step by Step Solution

1. Step 1: Write the proportion equation
   516.56 : 766.69 = 766.69 : x
2. Step 2: Convert to fraction form
   516.56/766.69 = 766.69/x
3. Step 3: Cross multiply
   516.56x = 766.69 × 766.69
4. Step 4: Simplify right side
   516.56x = 587,809.72
5. Step 5: Solve for x
   x = 587,809.72/516.56
6. Step 6: Final answer
   x = 1,137.93