Finding the Third Proportional to 253.50 and 410.50

Step by Step Solution

1. Step 1: Write the proportion equation
   253.50 : 410.50 = 410.50 : x
2. Step 2: Convert to fraction form
   253.50/410.50 = 410.50/x
3. Step 3: Cross multiply
   253.50x = 410.50 × 410.50
4. Step 4: Simplify right side
   253.50x = 168,510.25
5. Step 5: Solve for x
   x = 168,510.25/253.50
6. Step 6: Final answer
   x = 664.73