A movie theater has a seating capacity of 289.

Question

A movie theater has a seating capacity of 289. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2090, How many children, students, and adults attended?

children attended.

   students attended.

   adults attended.

Answer 1

Let C, S and A be the number of children, students and adults.

C+S+A=289

A = C/2

C+S+C/2=289

3C+2S = 578 EQN 1

C = (578-2S)/3

5C+7S+12A = 2090

5C+7S+6C=2090

11C+7S=2090 EQN 2

11(578-2S)/3+7S=2090

11(578-2S)+21S=6270

6358-22S+21S=6270

S=6358-6270=88

Substituting 88 into EQN 1

3C+2(88)=578

3C = 578-176 =402

C=402/3=134

A=134/2 = 67

134 Children attended

88 Students attended

67 Adults attended

Answer 2

5C+7S+12A =2090

A=C/2

A+S+A=289

3 equations, 3 unknowns,

use matrix algebra and row operations

or substitution and elimination

134+88+67=289

134=2(67)

5(134)+7(88)+12(67)=670+616+804=2090

`134 children

88 students

67 adults