Finding the Third Proportional to 401.63 and 842.63

Step by Step Solution

1. Step 1: Write the proportion equation
   401.63 : 842.63 = 842.63 : x
2. Step 2: Convert to fraction form
   401.63/842.63 = 842.63/x
3. Step 3: Cross multiply
   401.63x = 842.63 × 842.63
4. Step 4: Simplify right side
   401.63x = 710,016.89
5. Step 5: Solve for x
   x = 710,016.89/401.63
6. Step 6: Final answer
   x = 1,767.86