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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.

Respuesta :

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

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