Finding the Third Proportional to 772.69 and 1,823.16

Step by Step Solution

1. Step 1: Write the proportion equation
   772.69 : 1,823.16 = 1,823.16 : x
2. Step 2: Convert to fraction form
   772.69/1,823.16 = 1,823.16/x
3. Step 3: Cross multiply
   772.69x = 1,823.16 × 1,823.16
4. Step 4: Simplify right side
   772.69x = 3,323,898.71
5. Step 5: Solve for x
   x = 3,323,898.71/772.69
6. Step 6: Final answer
   x = 4,301.74