Finding the Third Proportional to 407.50 and 419.50

Step by Step Solution

1. Step 1: Write the proportion equation
   407.50 : 419.50 = 419.50 : x
2. Step 2: Convert to fraction form
   407.50/419.50 = 419.50/x
3. Step 3: Cross multiply
   407.50x = 419.50 × 419.50
4. Step 4: Simplify right side
   407.50x = 175,980.25
5. Step 5: Solve for x
   x = 175,980.25/407.50
6. Step 6: Final answer
   x = 431.85