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.
