Finding the Third Proportional to 259.50 and 697.50

Step by Step Solution

1. Step 1: Write the proportion equation
   259.50 : 697.50 = 697.50 : x
2. Step 2: Convert to fraction form
   259.50/697.50 = 697.50/x
3. Step 3: Cross multiply
   259.50x = 697.50 × 697.50
4. Step 4: Simplify right side
   259.50x = 486,506.25
5. Step 5: Solve for x
   x = 486,506.25/259.50
6. Step 6: Final answer
   x = 1,874.78