Finding the Third Proportional to 537 and 1,033.50

Step by Step Solution

1. Step 1: Write the proportion equation
   537 : 1,033.50 = 1,033.50 : x
2. Step 2: Convert to fraction form
   537/1,033.50 = 1,033.50/x
3. Step 3: Cross multiply
   537x = 1,033.50 × 1,033.50
4. Step 4: Simplify right side
   537x = 1,068,122.25
5. Step 5: Solve for x
   x = 1,068,122.25/537
6. Step 6: Final answer
   x = 1,989.05