Finding the Third Proportional to 442.50 and 523.50

Step by Step Solution

1. Step 1: Write the proportion equation
   442.50 : 523.50 = 523.50 : x
2. Step 2: Convert to fraction form
   442.50/523.50 = 523.50/x
3. Step 3: Cross multiply
   442.50x = 523.50 × 523.50
4. Step 4: Simplify right side
   442.50x = 274,052.25
5. Step 5: Solve for x
   x = 274,052.25/442.50
6. Step 6: Final answer
   x = 619.33