Finding the Fourth Proportional to 1,223.16, 1,689.35 and 829.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,223.16 : 1,689.35 = 829.50 : x
2. Step 2: Convert to fraction form
   1,223.16/1,689.35 = 829.50/x
3. Step 3: Cross multiply
   1,223.16x = 1,689.35 × 829.50
4. Step 4: Simplify right side
   1,223.16x = 1,401,310.01
5. Step 5: Solve for x
   x = 1,401,310.01/1,223.16
6. Step 6: Final answer
   x = 1,145.65