Finding the Third Proportional to 409.78 and 823.78

Step by Step Solution

1. Step 1: Write the proportion equation
   409.78 : 823.78 = 823.78 : x
2. Step 2: Convert to fraction form
   409.78/823.78 = 823.78/x
3. Step 3: Cross multiply
   409.78x = 823.78 × 823.78
4. Step 4: Simplify right side
   409.78x = 678,615.55
5. Step 5: Solve for x
   x = 678,615.55/409.78
6. Step 6: Final answer
   x = 1,656.04