Finding the Third Proportional to 516.50 and 779.50

Step by Step Solution

1. Step 1: Write the proportion equation
   516.50 : 779.50 = 779.50 : x
2. Step 2: Convert to fraction form
   516.50/779.50 = 779.50/x
3. Step 3: Cross multiply
   516.50x = 779.50 × 779.50
4. Step 4: Simplify right side
   516.50x = 607,620.25
5. Step 5: Solve for x
   x = 607,620.25/516.50
6. Step 6: Final answer
   x = 1,176.42