Finding the Third Proportional to 829.69 and 1,098.56

Step by Step Solution

1. Step 1: Write the proportion equation
   829.69 : 1,098.56 = 1,098.56 : x
2. Step 2: Convert to fraction form
   829.69/1,098.56 = 1,098.56/x
3. Step 3: Cross multiply
   829.69x = 1,098.56 × 1,098.56
4. Step 4: Simplify right side
   829.69x = 1,206,839.57
5. Step 5: Solve for x
   x = 1,206,839.57/829.69
6. Step 6: Final answer
   x = 1,454.57