Finding the Third Proportional to 514.69 and 649.69

Step by Step Solution

1. Step 1: Write the proportion equation
   514.69 : 649.69 = 649.69 : x
2. Step 2: Convert to fraction form
   514.69/649.69 = 649.69/x
3. Step 3: Cross multiply
   514.69x = 649.69 × 649.69
4. Step 4: Simplify right side
   514.69x = 422,093.85
5. Step 5: Solve for x
   x = 422,093.85/514.69
6. Step 6: Final answer
   x = 820.10