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

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

To start with, the football team has 30 more players than the basketball team, so the number of players on the football team is 30 + y.

Then you have to add on the extra ten players to each team so that the ratio fits. Now the football team is 10 + 30 + y (or 40 + y) and the basketball team is 10 + y.

Next you need to divide the ratio by its respective parts since a third of the football team is equal to half of the basketball team. So you end up with this equation:

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

You can multiply the three over to the other side to cancel it out. Same with the two. So, now the equation is:

80 + 2y = 30 + 3y

Subtract the 30 from the 80 and the 2y from the 3y and you have your answer: y = 50.

Go back up to the top where you found out that x = 30 + y and put the 50 in place of the y, giving you x = 80.