Finding the Third Proportional to 684 and 1,046.50

Step by Step Solution

1. Step 1: Write the proportion equation
   684 : 1,046.50 = 1,046.50 : x
2. Step 2: Convert to fraction form
   684/1,046.50 = 1,046.50/x
3. Step 3: Cross multiply
   684x = 1,046.50 × 1,046.50
4. Step 4: Simplify right side
   684x = 1,095,162.25
5. Step 5: Solve for x
   x = 1,095,162.25/684
6. Step 6: Final answer
   x = 1,601.11