Finding the Third Proportional to 142.50 and 257.50

Step by Step Solution

1. Step 1: Write the proportion equation
   142.50 : 257.50 = 257.50 : x
2. Step 2: Convert to fraction form
   142.50/257.50 = 257.50/x
3. Step 3: Cross multiply
   142.50x = 257.50 × 257.50
4. Step 4: Simplify right side
   142.50x = 66,306.25
5. Step 5: Solve for x
   x = 66,306.25/142.50
6. Step 6: Final answer
   x = 465.31