Finding the Third Proportional to 852 and 1,288.50

Step by Step Solution

1. Step 1: Write the proportion equation
   852 : 1,288.50 = 1,288.50 : x
2. Step 2: Convert to fraction form
   852/1,288.50 = 1,288.50/x
3. Step 3: Cross multiply
   852x = 1,288.50 × 1,288.50
4. Step 4: Simplify right side
   852x = 1,660,232.25
5. Step 5: Solve for x
   x = 1,660,232.25/852
6. Step 6: Final answer
   x = 1,948.63