Finding the Third Proportional to 405 and 641.50

Step by Step Solution

1. Step 1: Write the proportion equation
   405 : 641.50 = 641.50 : x
2. Step 2: Convert to fraction form
   405/641.50 = 641.50/x
3. Step 3: Cross multiply
   405x = 641.50 × 641.50
4. Step 4: Simplify right side
   405x = 411,522.25
5. Step 5: Solve for x
   x = 411,522.25/405
6. Step 6: Final answer
   x = 1,016.10