Travis is 17 years older than his sister Kate. In 11 years, he will be twice as old as Kate. How old is each of them now?

Answer 1

Being able to write the relationship between the two ages is the key to your equations. Sometimes this is where we get stuck, even though we understand the relationship.

So, if Travis is 17 years older than Kate, let's give Travis an age and this will tell us how to write our equation.

Let's say Travis is 20, that would make Kate 3. So, Travis' age = Kate's age + 17

T= K + 17

Then, after 11 years, Travis is twice as old as Kate.

This sentence says T + 11 (Travis in 11 years) = (is) 2 (twice as old) K + 11 (as Kate in 11 years)

T + 11 = 2 (K + 11)

T + 11 = 2K + 22

T = 2K + 11

Now take your 1st equation and substitute the value of T into the 2nd equation so that you have only one variable.

T = K + 17 and T = 2K + 11

K + 17 = 2K + 11 and solve for K

K = 6 so, T = 23

And in 11 years, Kate will be 17 and Travis will be 34 (twice as old).

Answer 2

T=17+K T is now 17 more than K

T+11 = 2(K+11) in 11 years Travis will be twice Kate's age

T+11 = 2K+22

T=2K +11

17+K = 2K +11

K=6

T=23

in 11 years K=17, T=34

34=2(17)

Kate is now 6 years old, Travis is now 23 years old