Finding the Third Proportional to 589.50 and 687.38

Step by Step Solution

1. Step 1: Write the proportion equation
   589.50 : 687.38 = 687.38 : x
2. Step 2: Convert to fraction form
   589.50/687.38 = 687.38/x
3. Step 3: Cross multiply
   589.50x = 687.38 × 687.38
4. Step 4: Simplify right side
   589.50x = 472,484.39
5. Step 5: Solve for x
   x = 472,484.39/589.50
6. Step 6: Final answer
   x = 801.50