The football team has 30 more members than the basketball teams. if each group had 10 more members, the ratio of their membership would be 3.2. how many members are in each group? write your answer as football x basketball y

We start with football =basketball +30 of x=y+30
Add 10 so that 3/2=(f+10)/(y+10) 
Now let's use substitution to get 3/2=(y+30+10)/(y+10) or 3/2=(y+40)/(y+10) 
Now cross multiply so 3(y+10)=2(y+40) or 3y+30=2y+80. Solve to get y=50, meaning x must be 80.
Now let's check to make sure it would be 3/2 if each gets 10 new members. Football would then have 90 and basketball would have 60, so yes, it works!!