Assign two variables for each problem, and write the equations. solve.

in five years, kate will be twice as old as joey. right now, kate is 11 years older than joey. how old is joey right now?

i need two variables and two equations. and solve it.

Lets make k equal to Kate's age and j equal to Joey's age.  If in 5 years Kate will be twice as old as Joe, you can write the equation k+5=2(j+5) and then simplify it to make it easier to work with.
k+5=2(j+5)
k+5=2j+10
k+5-2j=10
k-2j=5
since we know that right know Kate is 11 years older than Joey, you can write the equation k+j=11.  Since you know have two equations with with the same variable, you can make a system of equations as fallows:
k-2j=5
k+j=11

Since you need to figure out how old Joey is, you need to somehow get k to cancel out.  The easiest thing to do for this problem is to is multiply the top equation by -1 to get:
-k+2j=-5   (you have to add the bottom equation to the top equation)
k+j=11     (-k+k=0, 2j+j=3j, and -5+11=6)
Since k got canceled out, you are left with the equation 3j=6 which means j=2.
Therefore, Joey's current age is 2.

I hope this helps.

Step-by-step explanation:

The first answer is correct because you are really not changing anything about the question