Finding the Third Proportional to 493.50 and 589.50

Step by Step Solution

1. Step 1: Write the proportion equation
   493.50 : 589.50 = 589.50 : x
2. Step 2: Convert to fraction form
   493.50/589.50 = 589.50/x
3. Step 3: Cross multiply
   493.50x = 589.50 × 589.50
4. Step 4: Simplify right side
   493.50x = 347,510.25
5. Step 5: Solve for x
   x = 347,510.25/493.50
6. Step 6: Final answer
   x = 704.17