Finding the Third Proportional to 825 and 1,466.50

Step by Step Solution

1. Step 1: Write the proportion equation
   825 : 1,466.50 = 1,466.50 : x
2. Step 2: Convert to fraction form
   825/1,466.50 = 1,466.50/x
3. Step 3: Cross multiply
   825x = 1,466.50 × 1,466.50
4. Step 4: Simplify right side
   825x = 2,150,622.25
5. Step 5: Solve for x
   x = 2,150,622.25/825
6. Step 6: Final answer
   x = 2,606.81