Finding the Third Proportional to 410.25 and 457.50

Step by Step Solution

1. Step 1: Write the proportion equation
   410.25 : 457.50 = 457.50 : x
2. Step 2: Convert to fraction form
   410.25/457.50 = 457.50/x
3. Step 3: Cross multiply
   410.25x = 457.50 × 457.50
4. Step 4: Simplify right side
   410.25x = 209,306.25
5. Step 5: Solve for x
   x = 209,306.25/410.25
6. Step 6: Final answer
   x = 510.19