Question

Bayside High School Orchestra performed two concerts to raise money for a field trip. Tickets were $8 for

adults and $5 for students and teachers. In total, 423 people attended both concerts, and the orchestra raised
$2616. The number of teachers who came was a third of the number of students. Which of the following
systems can be used to represent this situation?

Answer 1

Adults = 167

Students = 256

Teachers = 85

Explanation:

Let:

S represents Students

A represents Adults

T represents Teachers

From the instructions in the question, we have that:

`A + S = 423` -- (1)

`8A + 5S = 2616` -- (2)

Make A the subject in (1)

`A + S = 423`

`A = 423 - S`

Substitute
`423 - S` for A in (2)

`8A + 5S = 2616`

`8(423 - S) + 5S = 2616`

Open Bracket

`3384 - 8S + 5S = 2616`

`3384 -3S = 2616`

Solve for S

`-3S = 2616 - 3384`

`-3S = -768`

`S = -768/-3`

`S = 256`

Recall that
`A = 423 - S`

`A = 423 - 256`

`A = 167`

From the question, we understand that;

`T = (1)/(3)S`

`T = (1)/(3) * 256`

`T = 85.333`

`T = 85` (Approximated)