let Brian's wage pumping gas be $x
then his wage tutoring is $2x
his sister's wage is 2x/4 = x/2
"His total weekly wages are $150 more than that of his younger sister"
If found that a lot of students have difficulty with that kind of a statement.
They don't know whether to add/subtact the $150.
I used to have my students translate the above into something like...
His wages are greater than the sister's wages by 150
---> x + 2x > x/2 by 150
so to make that statement into an equation we would add the 150 to the smaller side or ...
x+2x = x/2 + 150
3x = x/2+150
6x = x+300
5x = 300
x = 60
so Brian earns 2x as a tutor or $120
Brian pumping gas : 60
Brian tutoring : 120
total of his wages = 180
sister : half of his tutoring or 30
does Brian make 150 more than the sister ? YES!
thank you so much