Finding the Third Proportional to 506 and 799.50

Step by Step Solution

1. Step 1: Write the proportion equation
   506 : 799.50 = 799.50 : x
2. Step 2: Convert to fraction form
   506/799.50 = 799.50/x
3. Step 3: Cross multiply
   506x = 799.50 × 799.50
4. Step 4: Simplify right side
   506x = 639,200.25
5. Step 5: Solve for x
   x = 639,200.25/506
6. Step 6: Final answer
   x = 1,263.24