Finding the Third Proportional to 412.50 and 456.75

Step by Step Solution

1. Step 1: Write the proportion equation
   412.50 : 456.75 = 456.75 : x
2. Step 2: Convert to fraction form
   412.50/456.75 = 456.75/x
3. Step 3: Cross multiply
   412.50x = 456.75 × 456.75
4. Step 4: Simplify right side
   412.50x = 208,620.56
5. Step 5: Solve for x
   x = 208,620.56/412.50
6. Step 6: Final answer
   x = 505.75