Finding the Third Proportional to 421.50 and 456.50

Step by Step Solution

1. Step 1: Write the proportion equation
   421.50 : 456.50 = 456.50 : x
2. Step 2: Convert to fraction form
   421.50/456.50 = 456.50/x
3. Step 3: Cross multiply
   421.50x = 456.50 × 456.50
4. Step 4: Simplify right side
   421.50x = 208,392.25
5. Step 5: Solve for x
   x = 208,392.25/421.50
6. Step 6: Final answer
   x = 494.41