Finding the Third Proportional to 319.78 and 682.59

Step by Step Solution

1. Step 1: Write the proportion equation
   319.78 : 682.59 = 682.59 : x
2. Step 2: Convert to fraction form
   319.78/682.59 = 682.59/x
3. Step 3: Cross multiply
   319.78x = 682.59 × 682.59
4. Step 4: Simplify right side
   319.78x = 465,934.23
5. Step 5: Solve for x
   x = 465,934.23/319.78
6. Step 6: Final answer
   x = 1,457.04