Finding the Third Proportional to 820 and 1,269.50

Step by Step Solution

1. Step 1: Write the proportion equation
   820 : 1,269.50 = 1,269.50 : x
2. Step 2: Convert to fraction form
   820/1,269.50 = 1,269.50/x
3. Step 3: Cross multiply
   820x = 1,269.50 × 1,269.50
4. Step 4: Simplify right side
   820x = 1,611,630.25
5. Step 5: Solve for x
   x = 1,611,630.25/820
6. Step 6: Final answer
   x = 1,965.40