Finding the Third Proportional to 2,005 and 2,821.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,005 : 2,821.50 = 2,821.50 : x
2. Step 2: Convert to fraction form
   2,005/2,821.50 = 2,821.50/x
3. Step 3: Cross multiply
   2,005x = 2,821.50 × 2,821.50
4. Step 4: Simplify right side
   2,005x = 7,960,862.25
5. Step 5: Solve for x
   x = 7,960,862.25/2,005
6. Step 6: Final answer
   x = 3,970.50