how old they are?

Let's have b = current brother's age and s = current sister's age.

The brothers age is twice his sisters age, so we have:

b = 2s

In 6 years, the brothers age will be 5 times his sisters age...as she was 3 years ago.

6 + b = 5(s-3)              ---Now just simplify a little bit

6 + b = 5s - 15

21 + b = 5s

 

So how we have two equations.

b = 2s 

and

21 + b = 5s

 

Let's solve this by elimiation. Multiply the first equation by a negative

b = 2s 

-b = -2s

21 + b = 5s          ---Second equation

21 = 3s

7 = s

 

The sisters age is 7. Let's put in this for s in the first equation and solve for b (which is the brothers age)

b = 2s 

b = 2(7)

b = 14

 

So the sister is 7 years old and the brother is 14 years old.