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

Write a system of linear equations that represents the 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

Answer 1

The system of equations are
`x+y=64` and
`x=y+10`

Explanation:

Given : 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.

To find : Write a system of linear equations that represents the situation.

Solution :

Let x represent the number of students in the drama club

and y represent the number of students in the yearbook club.

There are a total of 64 students in a drama club and a yearbook club.

i.e.
`x+y=64` ....(1)

The drama club has 10 more students than the yearbook club.

i.e.
`x=y+10` ....(2)

Substitute the value of (2) in (1),

`y+10+y=64`

`2y=54`

`y=(54)/(2)`

`y=27`

Substitute in (2),

`x=27+10`

`x=37`

Therefore, the system of equations are
`x+y=64` and
`x=y+10`