college algebra linear systems

Question

Nate is 6 years older than Haley. In 3 years the sum of their ages will be 62. How old is Nate now?

Answer 1

If we let N be the age of Nate and H be the age of Haley, what we're given in the problem translates into two equations:

N = H+6 (Nate is 6 years older than Haley)

(N+3)+(H+3) = 62 (In 3 years the sum of their ages will be 62)

N-H = 6 and N+H+6 = 62, which means N-H = 6 and N+H = 56.

If we add these two equations together to get another equivalent and more useful equation, we get that:

(N-H)+(N+H) = 56 + 6 which means 2N = 62, so N = 31, so Nate is currently 31 years old.