Question

There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club.

a. Write a system of linear equations that represents this situation. Let x represent the number of students in the drama club and y represent the number of students in the yearbook club.

System of equations: x=
a



a
x+
a
y=64

Question 2
b. How many students are in the drama club? the yearbook club?

There are
students in the drama club.

There are
students in the yearbook club.

Answer 1

Q1)

x + y = 64

x = y + 10

Q2)

Students in drama club: 37

Students in Yearbook club: 27

Explanation:

Students in drama club: x

Students in Yearbook club: y

x + y = 64

x = y + 10

y + 10 + y = 64

2y = 54

y = 27

x = 27 + 10 = 37

Answer 2

x+y = 64

x = y+10

37 drama students

27 yearbook students

Explanation:

Let x represent the number of students in the drama club

y represent the number of students in the yearbook club.

x+y = 64 since there are 64 students

x = y+10 since there are 10 more drama members

Now lets solve

Substituting the second equation into the first equation

x+y = 64

(y+10) +y = 64

Combine like terms

2y+10 = 64

Subtract 10 from each side

2y+10-10 = 64-10

2y = 54

Divide each side by 2

2y/2 = 54/2

y = 27

Now solve for x

x = y+10

x = 27+10

x = 37