Finding the Third Proportional to 469.69 and 829.69

Step by Step Solution

1. Step 1: Write the proportion equation
   469.69 : 829.69 = 829.69 : x
2. Step 2: Convert to fraction form
   469.69/829.69 = 829.69/x
3. Step 3: Cross multiply
   469.69x = 829.69 × 829.69
4. Step 4: Simplify right side
   469.69x = 688,381.35
5. Step 5: Solve for x
   x = 688,381.35/469.69
6. Step 6: Final answer
   x = 1,465.62