Finding the Third Proportional to 506.81 and 724.78

Step by Step Solution

1. Step 1: Write the proportion equation
   506.81 : 724.78 = 724.78 : x
2. Step 2: Convert to fraction form
   506.81/724.78 = 724.78/x
3. Step 3: Cross multiply
   506.81x = 724.78 × 724.78
4. Step 4: Simplify right side
   506.81x = 525,307.86
5. Step 5: Solve for x
   x = 525,307.86/506.81
6. Step 6: Final answer
   x = 1,036.49