Question

John’s age in 5 years time will be the same as Jack’s age is now. In two years, Jack will be twice as old as John. How old are they now?

Answer 1

John is 3 and Jack is 8.

Let n be John's age and k be Jack's age.

John's age in 5 years would be represented as n+5; this gives us n+5=k.
John's age in 2 years would be n+2 and Jack's age in 2 years would be k+2; this gives us
k+2=2(n+2)
Using the distributive property,

k+2=2*n+2*2
k+2=2n+4

Substituting our value of k from the first equation,
n+5+2=2n+4

Combining like terms,
n+7=2n+4

Subtract n from both sides:
n+7-n=2n+4-n
7=n+4

Subtract 4 from both sides:
7-4=n+4-4
3=n

n+5=k
3+5=k
8=k