Question

 If you add​ Natalie's age and​ Fred's age, the result is 37. If you add​ Fred's age to 3 times​ Natalie's age, the result is 63. Write and solve a system of equations to find how old Fred and Natalie are??

Answer 1

Natalie is 13 Fred is 24

Explanation:

Let `x` be Fred and `y` be Natalie
Rewrite the written problem into algebraic form.
`x+y=37`
`x+3y=63`
We can then rewrite these equations
As `x+y=37` we can rewrite the second equation with that in mind
`2y+37=63` (we replaced an `x` and `y` with `37`)
Solve from here
`2y=63-37`
`2y=26`
`y=13`
We now know Natalie's age, putting that into the first equation of
`x+y=37`
We get
`x+13=37`
`x=37-13`
`x=24`
And that is Fred's age