Question

there a total of 94 students in a drama club and a yearbook club. the drama club has 10 more students than the yearbook club. How many students are in the drama club? the yearbook club?

Answer 1

d = amount of drama club students.

y = amount of yearbook students

we know their total is 94, thus d + y = 94.

but we also know that whatever "y" is, "d" is 10 more than that, d = y + 10.


`\bf \begin{cases} d+y=94\\ \boxed{d}=y+10\\ --------\\ \boxed{y+10}+y=94 \end{cases} \\\\\\ 2y=84\implies y=\cfrac{84}{2}\implies y=42`

how many are there in the drama club? well, d = y + 10.

Answer 2

Let d and y represent the numbers of students in the drama and yearbook clubs, respectively. The problem statement gives rise to two equations:
d +y = 94
d -y = 10

Adding these two equations we find
2d = 104
d = 52
Then
y = d -10 = 42

There are 52 students in the drama club.
There are 42 students in the yearbook club.