Finding the Third Proportional to 724 and 1,089.50

Step by Step Solution

1. Step 1: Write the proportion equation
   724 : 1,089.50 = 1,089.50 : x
2. Step 2: Convert to fraction form
   724/1,089.50 = 1,089.50/x
3. Step 3: Cross multiply
   724x = 1,089.50 × 1,089.50
4. Step 4: Simplify right side
   724x = 1,187,010.25
5. Step 5: Solve for x
   x = 1,187,010.25/724
6. Step 6: Final answer
   x = 1,639.52