How many members are in each group?

Question

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

Answer 1

Let x = # people on football team

Let y = # people on basketball team

 

Since Football has 30 more people than basketball then  x = y+30

 

Adding 10 more people to each team would make the ration  3:2 

 

10 more on each team gives us totals of  x+10 and y+10

 

(x+10)/(y+10) = 3/2

substitute  y+30 in place of x giving

(y+30+10)/(y+10) = 3/2

(y+40)/(y+10) = 3/2

Cross multiply

2(y+40) = 3(y+10)

2y+80=3y+30

y = 50

 

x = y+30 = 80

 

There are 80 people on football teams and 50 on basketball

 

x = 80

y = 50