Finding the Third Proportional to 770 and 1,463.50

Step by Step Solution

1. Step 1: Write the proportion equation
   770 : 1,463.50 = 1,463.50 : x
2. Step 2: Convert to fraction form
   770/1,463.50 = 1,463.50/x
3. Step 3: Cross multiply
   770x = 1,463.50 × 1,463.50
4. Step 4: Simplify right side
   770x = 2,141,832.25
5. Step 5: Solve for x
   x = 2,141,832.25/770
6. Step 6: Final answer
   x = 2,781.60