Maggie's brother is 5 years younger than three times her age. The sum of their ages is 51.

How old is Maggie?

Let us denote Maggie's years with M and her brother's years with Y.

We know that Maggie's brother is 5 years younger than three times her age. So, we can write:

Y=3*M-5 (1)

We also know that the sum of their ages is 51, so we can write:

Y+M=51 (2)

We can put the first equation (1) in the second (2) and we will obtain:

3M-5+M=51

4M-5=51

4M=51+5

4M=56

M=56/4

M=14

Maggie is 14 years old.

And her brother is : Y=51-14=34 years old.