Finding the Third Proportional to 823.50 and 1,764

Step by Step Solution

1. Step 1: Write the proportion equation
   823.50 : 1,764 = 1,764 : x
2. Step 2: Convert to fraction form
   823.50/1,764 = 1,764/x
3. Step 3: Cross multiply
   823.50x = 1,764 × 1,764
4. Step 4: Simplify right side
   823.50x = 3,111,696
5. Step 5: Solve for x
   x = 3,111,696/823.50
6. Step 6: Final answer
   x = 3,778.62