Max was on vacation twice as long as Jared and half as long as Wesley. The boys were on vacation a total of 3 weeks. How many days was each boy on vacation?

Lets say W=Wesley, M=Max, and J=Jared.

So your equations are M=2J, 2M=W, and M+J+W=21days (3 weeks)

So substituting M and W into M+J+W=21 gives you 2J+J+2M=21, substitute M again, to get 2J+J+4J=21 so you get 7J=21 so J = 3 days. Using J=3, substitute in to find M, using M=2J, so M=2 (3) so M=6 and using that, substitute into 2M=W, so 2 (6) = W so W=12. And 12+6+3=21 to check.