Question 1173699
Let's say Kurt's age is k and Vince's age is v. We can use these variables to create equations to help us solve the problem.
We have two pieces of information. In 5 years Kurt will be twice as only as Vince:(k+5)=2(v+5) and 5 years ago, Kurt was three times as old as Vince: (k-5)=3(v-5)

(k+5)=2(v+5)
k+5=2v+10
k-2v=5
k=5+2v (now that we have solved for k we can use it for the next equation so we are only dealing with one variable at a time.

(k-5)=3(v-5)
k-5=3v-15
k-3v=-10 (simplify this equation as much as possible)
(5+2v)-3v=-10 (input 5+2v instead of k so we can solve for v)
5-v=-10
-v=-15
v=15 (Vince is 15 years old)

Now we can use one of the first equations to solve for Kurt's age. Let's take (k+5)=2(v+5)
k+5=2(15+5) (we replace v with 15 because we know that v=15)
k+5=40
k=35 (Kurt is 35 years old)

To check our work we can use the second equation to see if we are correct.
(k-5)=3(v-5)
35-5=3(15-5) (we replace k with 35 and v with 15)
30=30 (since they are equal we know our answers are correct)

Therefore Vince is 15 years old and Kurt is 35 years old.