Finding the Third Proportional to 380.50 and 821.50

Step by Step Solution

1. Step 1: Write the proportion equation
   380.50 : 821.50 = 821.50 : x
2. Step 2: Convert to fraction form
   380.50/821.50 = 821.50/x
3. Step 3: Cross multiply
   380.50x = 821.50 × 821.50
4. Step 4: Simplify right side
   380.50x = 674,862.25
5. Step 5: Solve for x
   x = 674,862.25/380.50
6. Step 6: Final answer
   x = 1,773.62