Finding the Third Proportional to 769.50 and 1,238.63

Step by Step Solution

1. Step 1: Write the proportion equation
   769.50 : 1,238.63 = 1,238.63 : x
2. Step 2: Convert to fraction form
   769.50/1,238.63 = 1,238.63/x
3. Step 3: Cross multiply
   769.50x = 1,238.63 × 1,238.63
4. Step 4: Simplify right side
   769.50x = 1,534,191.89
5. Step 5: Solve for x
   x = 1,534,191.89/769.50
6. Step 6: Final answer
   x = 1,993.75