Finding the Third Proportional to 256.50 and 514.50

Step by Step Solution

1. Step 1: Write the proportion equation
   256.50 : 514.50 = 514.50 : x
2. Step 2: Convert to fraction form
   256.50/514.50 = 514.50/x
3. Step 3: Cross multiply
   256.50x = 514.50 × 514.50
4. Step 4: Simplify right side
   256.50x = 264,710.25
5. Step 5: Solve for x
   x = 264,710.25/256.50
6. Step 6: Final answer
   x = 1,032.01