Finding the Third Proportional to 259.50 and 677.25

Step by Step Solution

1. Step 1: Write the proportion equation
   259.50 : 677.25 = 677.25 : x
2. Step 2: Convert to fraction form
   259.50/677.25 = 677.25/x
3. Step 3: Cross multiply
   259.50x = 677.25 × 677.25
4. Step 4: Simplify right side
   259.50x = 458,667.56
5. Step 5: Solve for x
   x = 458,667.56/259.50
6. Step 6: Final answer
   x = 1,767.51