Finding the Third Proportional to 311.50 and 511.50

Step by Step Solution

1. Step 1: Write the proportion equation
   311.50 : 511.50 = 511.50 : x
2. Step 2: Convert to fraction form
   311.50/511.50 = 511.50/x
3. Step 3: Cross multiply
   311.50x = 511.50 × 511.50
4. Step 4: Simplify right side
   311.50x = 261,632.25
5. Step 5: Solve for x
   x = 261,632.25/311.50
6. Step 6: Final answer
   x = 839.91