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Children at Large

Age 11 to 14
Challenge Level

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?