# There are a total of 64 students in either the drama club or the yearbook club (none of the students are in both clubs). The drama club has 10 more students than the yearbook club. How many students are in each club?

Jan 30, 2018

37 students in the drama club, 27 in the yearbook club.

#### Explanation:

a=number of students in the drama club
b=number of students in the yearbook club

$a + b = 64$
$\textcolor{red}{a - 10 = b}$
Subtract the equations
$\cancel{a \textcolor{red}{- a}} + b \textcolor{red}{+ 10} = 64 \textcolor{red}{- b}$
$b + 10 = 64 - b$
$b \textcolor{red}{+ b} + \cancel{10 \textcolor{red}{- 10}} = 64 \textcolor{red}{- 10} \cancel{- b \textcolor{red}{+ b}}$
$2 b = 54$
$b = 27$
$a + 27 = 64$
$a = 64 - 27$
$a = 37$