Question

The swim and diving clubs at Riverdale High School have a total of 55 members and no student is a member of both teams. 1/3 of the swim team members are seniors and 1/5 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.

Answer 1

The first question x+y=55
The second question (1/3)x+(1/5)y=13
The third question 25 

Answer 2

We can write two equations from the given information.

Let x represent the total number of swim club members and let y represent the total number of diving club members

• "The swim and diving clubs at Riverdale High School have a total of 55 members"

$x+y=55$

• "1/3 of the swim team members are seniors and 1/5 of the diving team members are seniors. If there are 13 seniors in the two clubs..."

$\frac{1}{3} x +\frac{1}{5} y=13$

Solving these 2 equations simultaneously for x and y will give us the number of members in swim and diving clubs at Riverdale High School.

We can write first equation as $x=55-y$, and substitute x into the second equation to get,

$\frac{1}{3} (55-y)+\frac{1}{5} y=13\\\frac{55}{3} -\frac{1}{3}y +\frac{1}{5} y=13\\-\frac{2}{15} y=13-\frac{55}{3} \\-\frac{2}{15} y=-\frac{16}{3} \\y=40$

Since $x=55-y$, plugging in $y=40$ into this gives $x=15$.

ANSWER: Swim club has 15 members and Diving club has 40 members.