Finding the Third Proportional to 564 and 766.50

Step by Step Solution

1. Step 1: Write the proportion equation
   564 : 766.50 = 766.50 : x
2. Step 2: Convert to fraction form
   564/766.50 = 766.50/x
3. Step 3: Cross multiply
   564x = 766.50 × 766.50
4. Step 4: Simplify right side
   564x = 587,522.25
5. Step 5: Solve for x
   x = 587,522.25/564
6. Step 6: Final answer
   x = 1,041.71