Finding the Third Proportional to 823.88 and 1,777.69

Step by Step Solution

1. Step 1: Write the proportion equation
   823.88 : 1,777.69 = 1,777.69 : x
2. Step 2: Convert to fraction form
   823.88/1,777.69 = 1,777.69/x
3. Step 3: Cross multiply
   823.88x = 1,777.69 × 1,777.69
4. Step 4: Simplify right side
   823.88x = 3,160,172.85
5. Step 5: Solve for x
   x = 3,160,172.85/823.88
6. Step 6: Final answer
   x = 3,835.74