Finding the Third Proportional to 680 and 1,580.50

Step by Step Solution

1. Step 1: Write the proportion equation
   680 : 1,580.50 = 1,580.50 : x
2. Step 2: Convert to fraction form
   680/1,580.50 = 1,580.50/x
3. Step 3: Cross multiply
   680x = 1,580.50 × 1,580.50
4. Step 4: Simplify right side
   680x = 2,497,980.25
5. Step 5: Solve for x
   x = 2,497,980.25/680
6. Step 6: Final answer
   x = 3,673.50