Finding the Third Proportional to 538 and 632.50

Step by Step Solution

1. Step 1: Write the proportion equation
   538 : 632.50 = 632.50 : x
2. Step 2: Convert to fraction form
   538/632.50 = 632.50/x
3. Step 3: Cross multiply
   538x = 632.50 × 632.50
4. Step 4: Simplify right side
   538x = 400,056.25
5. Step 5: Solve for x
   x = 400,056.25/538
6. Step 6: Final answer
   x = 743.60