SOLUTION: According to​ statistics, a person will devote 35 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 17. Over the​ l

      Solution 1. The most simple and primitive


Let x be the number of year watching TV.
Then the number of years sleeping is (x+17).

The sum is 35 years

    x + (x+17) = 35.


Simplify and find x

    2x + 17 = 35

    2x = 35 - 17 = 18

     x = 18/2 = 9.


ANSWER.  Time for watching TW is 8 years; time for sleeping is 9+17 = 26 years.


CHECK.   Total time is 9 + 26 = 35 years.  ! correct !



      Solution 2. The most exiting and elegant


Let x be the number of year sleeping.
Let y be the number of year watching TV.


Write equations as you read the problem

    x + y = 35    (1)
    x - y = 17    (2)


To solve the system, add equations.  You will get

   2x = 35 + 17 = 52.


Hence, x = 52/2 = 26.


Thus, time sleeping is 26 years;  time watching TV is 35-26 = 9 years.


You get the same answer.



      Solution 3. Mental (without using equations)


When the sum (x+y) of two numbers x and y is given and their difference (x-y) is given,
then the numbers are half-sum and half difference of the given sum and the given difference

    x =  =  = 26;  y =  =  = 9.