Finding the Third Proportional to 381.50 and 513.50

Step by Step Solution

1. Step 1: Write the proportion equation
   381.50 : 513.50 = 513.50 : x
2. Step 2: Convert to fraction form
   381.50/513.50 = 513.50/x
3. Step 3: Cross multiply
   381.50x = 513.50 × 513.50
4. Step 4: Simplify right side
   381.50x = 263,682.25
5. Step 5: Solve for x
   x = 263,682.25/381.50
6. Step 6: Final answer
   x = 691.17