Question

There are four children in a family, two girls, Kate and sally, and two boys, tom and Ben.

tom is 2 years older than Ben.
The combined ages of the two boys is equal to the combined ages of the two girls.
Kate is twice as old as sally.
A year ago tom was twice as old as sally was then.
How old are the children now?

Answer 1

Bren=5 years

Tom=7yrs

Sally=4 yrs

Kate=8years

Explanation:

-Let Bren's current age be x, therefore Tom is x+2

-Let Sally's current age be y, therefore Kate is 2y

-Also, given that:

`x+x+2=2y+y\\\\2x+2=3y\ \ \ \ \ \ ...i`

#We calculate the ages one year ago of Tom and Sally:

`\#Tom's \age\\x+2-1=x+1\\\\\# Sally's \ age\\=y-1\\\\\therefore x+1=2(y-1)\\\\x=2y-3\ \ \ \ \ ...ii`

#Substitute for x in i;

`2x+2=3y\\\\2(2y-3)+2=3y\\\\4y-6+2=3y\\\\y=4\\\\2y=4* 2=8\\\\2x+2=4+8=12\\\\2x=10\\\\x=5\\\\(x+2)=7`