The swim and diving clubs at Riverdale High School have a total of 55 members and no student is a member of both teams. One-third of the swim team members are seniors and One-fifth of the diving team members are seniors. If there are 13 seniors in the two clubs, how many members does each club have? Let x represent the total number of swim club members and let y represent the total number of diving club members.

The equation that represents the total number of members is
.

The equation that represents the total number of seniors is
.

The diving club has
more members than the swim club.

You want the equations representing the relations that the total number of swim team members (x) and dive team members (y) is 55, and the number of seniors is 13, comprised of 1/3 of the swim team and 1/5 of the dive team. You also want to know the difference between y and x.

a. Members

Using the given variables to represent the numbers of team members, the equation for the total number of club members is ...

x + y = 55

b. Seniors

The sum of 1/3 of swim team members and 1/5 of dive team members is the number of seniors:

x/3 + y/5 = 13

c. Difference

We can multiply the second equation by 5 and subtract the first to find x:

5(x/3 +y/5) -(x +y) = 5(13) -(55)

2/3x = 10

x = 3/2·10 = 15

y = 55 -15 = 40

The diving club has 40 -15 = 25 more members than the swim club.