SOLUTION: Good day hope you are well Herewith my question:" Timothy is 8 years older then his sister, in 5 years from now she will be half Timothy's age. How old is timothy and his si

Let x be the Timothy's age, an let y be the sister's age.


Then from the condition, you have these two equations
    
    x = y + 8        (1)

    x+5 = 2*(y+5)    (2)



Substitute into equation (2) this expression for x of equation (1). You will get

    y + 8 = 2*(y+5)



Simplify and find y

    y + 8 + 5  = 2y + 10

    8 + 5 - 10 = 2y - y

        3      = y.


Thus the sister's age is 3 years.


From equation (1), then  x = 3 + 8 = 11 is the Tymothy's age.


ANSWER.  Tymothy is 11 years old;  the sister is 3 years old.

In 5 years, two events will happen simultaneously:


    Timothy will be 8 yeras older and two times as old as the sister.


    Hence, they will be  8 and 16 years old then.

    It means that now they are  8-5 = 3  and  16-5 = 11 years old.


You get the same answer