Finding the Third Proportional to 259 and 641.50

Step by Step Solution

1. Step 1: Write the proportion equation
   259 : 641.50 = 641.50 : x
2. Step 2: Convert to fraction form
   259/641.50 = 641.50/x
3. Step 3: Cross multiply
   259x = 641.50 × 641.50
4. Step 4: Simplify right side
   259x = 411,522.25
5. Step 5: Solve for x
   x = 411,522.25/259
6. Step 6: Final answer
   x = 1,588.89