Finding the Third Proportional to 766 and 1,653.50

Step by Step Solution

1. Step 1: Write the proportion equation
   766 : 1,653.50 = 1,653.50 : x
2. Step 2: Convert to fraction form
   766/1,653.50 = 1,653.50/x
3. Step 3: Cross multiply
   766x = 1,653.50 × 1,653.50
4. Step 4: Simplify right side
   766x = 2,734,062.25
5. Step 5: Solve for x
   x = 2,734,062.25/766
6. Step 6: Final answer
   x = 3,569.27