Finding the Third Proportional to 469.69 and 523.69

Step by Step Solution

1. Step 1: Write the proportion equation
   469.69 : 523.69 = 523.69 : x
2. Step 2: Convert to fraction form
   469.69/523.69 = 523.69/x
3. Step 3: Cross multiply
   469.69x = 523.69 × 523.69
4. Step 4: Simplify right side
   469.69x = 274,248.60
5. Step 5: Solve for x
   x = 274,248.60/469.69
6. Step 6: Final answer
   x = 583.90