Finding the Third Proportional to 688.50 and 1,022.63

Step by Step Solution

1. Step 1: Write the proportion equation
   688.50 : 1,022.63 = 1,022.63 : x
2. Step 2: Convert to fraction form
   688.50/1,022.63 = 1,022.63/x
3. Step 3: Cross multiply
   688.50x = 1,022.63 × 1,022.63
4. Step 4: Simplify right side
   688.50x = 1,045,761.89
5. Step 5: Solve for x
   x = 1,045,761.89/688.50
6. Step 6: Final answer
   x = 1,518.90