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.