Finding the Third Proportional to 259.50 and 389.56

Step by Step Solution

1. Step 1: Write the proportion equation
   259.50 : 389.56 = 389.56 : x
2. Step 2: Convert to fraction form
   259.50/389.56 = 389.56/x
3. Step 3: Cross multiply
   259.50x = 389.56 × 389.56
4. Step 4: Simplify right side
   259.50x = 151,758.94
5. Step 5: Solve for x
   x = 151,758.94/259.50
6. Step 6: Final answer
   x = 584.81