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=



x+
y=64

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

Answer 1

• x = y +10; x +y = 64
• x = 37; y = 27
• 37 in drama club; 27 in yearbook club

Explanation:

The equations will reflect the relations given in the problem statement:

x = y +10 . . . . . . 10 more in drama club than yearbook club

x + y = 64 . . . . . total of 64 students in both clubs

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If we use the first equation to substitute for x in the second equation, we get ...

(y +10) +y = 64

2y = 54 . . . . . . . subtract 10

y = 27 . . . . . . . divide by 2

x = y +10 = 27 +10 = 37

There are 37 students in the drama club; 27 in the yearbook club.