Start with the number 686.
Add three-fourths of a dozen.
Round to the nearest hundred.
Add half of 32.
Round to the nearest ten.
Add the digits in your number. The sum of that is your new number.
Triple that number.
Add the digits in your number. The sum of that is your new number.
Multiply by 10.
Divide that number in half.
Add the digits in your number. The sum of that is your new number.
Starting with 686, adding three-fourths of a dozen (9) gives us 695. Rounding to the nearest hundred gives us 700. Adding half of 32 (16) gives us 716. Rounding to the nearest ten gives us 720.
Adding the digits in 720 (7+2+0) gives us 9. Tripling that gives us 27. Adding the digits in 27 (2+7) gives us 9. Multiplying by 10 gives us 270. Dividing by 2 gives us 135. Adding the digits in 135 (1+3+5) gives us 9.
Final answer: 9.