Finding the Third Proportional to 500 and 659.50

Step by Step Solution

1. Step 1: Write the proportion equation
   500 : 659.50 = 659.50 : x
2. Step 2: Convert to fraction form
   500/659.50 = 659.50/x
3. Step 3: Cross multiply
   500x = 659.50 × 659.50
4. Step 4: Simplify right side
   500x = 434,940.25
5. Step 5: Solve for x
   x = 434,940.25/500
6. Step 6: Final answer
   x = 869.88