Finding the Third Proportional to 401.63 and 823.50

Step by Step Solution

1. Step 1: Write the proportion equation
   401.63 : 823.50 = 823.50 : x
2. Step 2: Convert to fraction form
   401.63/823.50 = 823.50/x
3. Step 3: Cross multiply
   401.63x = 823.50 × 823.50
4. Step 4: Simplify right side
   401.63x = 678,152.25
5. Step 5: Solve for x
   x = 678,152.25/401.63
6. Step 6: Final answer
   x = 1,688.52