Three kinds of tickets were sold for a concert. Child tickets are $6, adult tickets are $12, and student tickets are $8. A total of 204 tickets were sold, bringing in a total of $2,008. If 4 more adult tickets were sold than the total number of student and child tickets combined, how many student tickets were sold? Type in your numerical answer only; do not type any words or letters with your answer.

The number of children's tickets sold = 12 The number of adult's tickets sold = 100 The number of student's tickets sold = 92

Step-by-step explanation:

Let the number of children's tickets sold = c

Let the number of adult's tickets sold = a

Let the number of student's tickets sold = s

A total of 204 tickets were sold, therefore: c+a+s=204

Child tickets are $6, adult tickets are $12, and student tickets are $8.

Total revenue = $2,008

Therefore:

6c+12a+8s-2008

We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.

c+s=a+4

We then solve the resulting system of equation.

c+a+s=204 6c+12a+8s=2008 c+s=a+4

Substituting c+s=a+4 into the first equation

c+a+s=204

a+4+a=204

2a=204-4

2a=200

a=100

Substitute a=100 into the second and third equation

6c+12 (100) + 8s=2008

6c+8s=2008-1200

6c+8s=808

From the third equation

c+s=100+4

c=104-s

Substitute c=104-s into 6c+8s=808

6 (104-s) + 8s=808

624-6s+8s=808

2s=808-624

2s=184

s=92

Since c=104-s

c=104-92

c=12

Therefore:

The number of children's tickets sold = 12 The number of adult's tickets sold = 100 The number of student's tickets sold = 92