Question

The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing
with a total revenue of $1010. If the number of adult tickets sold was 10 less than twice the number of teacher tickets, how many of each
type of ticket were sold for the showing?
Define the variables for this situation. Use the variables a, t, and s.

Answer 1

Answer:

adults, a = 116

Students, s = 111

Teacher, t = 53

Step-by-step explanation:

Adult = $6

Teacher = $4

Students = $2

Let

Adults = a

Teacher = t

Students = s

Total revenue = $1010

Total tickets sold = 280

a = 2t - 10

a + s + t = 280

6a + 2s + 4t = 1010

Substitute a = 2t - 10 into the equation

2t - 10 + s + t = 280

6(2t - 10) + 2s + 4t = 1010

3t + s - 10 = 280

12t - 60 + 2s + 4t = 1010

3t + s = 280 + 10

16t + 2s = 1010 + 60

3t + s = 270 (1)

16t + 2s = 1070 (2)

Multiply (1) by 2

6t + 2s = 540 (3)

16t + 2s = 1070 (4)

Subtract (3) from (4)

16t - 6t = 1070 - 540

10t = 530

Divide both sides by 10

t = 530/10

= 53

t = 53

Substitute t =53 into (1)

3t + s = 270

3(53) + s = 270

159 + s = 270

s = 270 - 159

= 111

s = 111

Substitute the values of s = 111 and t = 53 into

a + s + t = 280

a + 111 + 53 = 280

a + 164 = 280

a = 280 - 164

= 116

adults, a = 116

Students, s = 111

Teacher, t = 53