The best way to go about this question is to give each person a variable. Let's call Brianna "B" and Julia "J" Since Joseph can't also be J, let's call him "S".
So we know that Brianna has 3 times as much money as Julia. We write this as B = 3 x J or just B = 3J
We also know that Julia has $12 more than Joseph. We write this as J = S + 12.
We also know they have $113 total. We write this as B + J + S = 113
Now, let's plug in what we know. B = 3J so B + J + S = 3J + J + S
J = S + 12 and we can subtract 12 from both sides to get S = J -12
so 3J + J + S = 3J + J + J - 12 = 5J -12 and we know this is equal to 113
so 5J-12 = 113. Add 12 to both sides to get 5J=125 and divide both sides by 5 to get J = 25.
But what are we looking for? How much money does Brianna have. So let's go back to B = 3 x J from the beginning and multiply 25 by 3 to get $75 as the amount Brianna has. You've got your answer!