We can look at this equation then fill in the variables as we go.
S+R+A=52
Each variable shows the number of points each person obtained(first letter of their name).
We know that sue scored 5 more than rose. S=5+R
(5+R)+R+A=52
Amy scored 9 less than sue. If the scored 9 less than sue, we can just subtract 9 from the equation 5+R=S
That means Amy scored 4 less than Rose.
(5+R)+R+(R-4)=52
5+R+R+R-4
3R+1=52
3R=51
R=17
Rose scored 17 points, which means Sue scored 22 since she scored 5 more. Amy scored 13 since she scored 9 less than Sue and 4 less than Rose. Let's check.
17+22+13=30+22=52
So, Rose scored 17 points, Sue scored 22 points, and Amy scored 13.