Finding the Third Proportional to 1,022 and 1,533.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,022 : 1,533.50 = 1,533.50 : x
2. Step 2: Convert to fraction form
   1,022/1,533.50 = 1,533.50/x
3. Step 3: Cross multiply
   1,022x = 1,533.50 × 1,533.50
4. Step 4: Simplify right side
   1,022x = 2,351,622.25
5. Step 5: Solve for x
   x = 2,351,622.25/1,022
6. Step 6: Final answer
   x = 2,301.00