Finding the Third Proportional to 766.50 and 1,164

Step by Step Solution

1. Step 1: Write the proportion equation
   766.50 : 1,164 = 1,164 : x
2. Step 2: Convert to fraction form
   766.50/1,164 = 1,164/x
3. Step 3: Cross multiply
   766.50x = 1,164 × 1,164
4. Step 4: Simplify right side
   766.50x = 1,354,896
5. Step 5: Solve for x
   x = 1,354,896/766.50
6. Step 6: Final answer
   x = 1,767.64