Question

A movie theater has a seating capacity of 187. 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 $ 1356, How
many children, students, and adults attended?​

Answer 1

Answer:

Number of children in theater   = 94

Number of students   = 46

Number of adults in theater= 47

Step-by-step explanation:

Total seating capacity in the theater = 187

Let us assume the number of students in the theater = m

and assume  the number of children in the theater = 2k

So, the number of adults in theater = Half of number of children = 2k/2 = k

⇒ Number of ( Adults + Children + students) = 187

⇒ k  + 2k + m =  187, or 3k + m = 187

Cost of 1 adult ticket = $12

So, the cost of k adult tickets = 12 x (k)  = $12k

Cost of 1 student ticket = $7

So, the cost of m student ticket = 7 x (m)  = $7m

Cost of 1 children  ticket = $5

So, the cost of 2k children tickets = 5 x (2k)  = $10k

⇒ 12k  + 10k + 7m =  1356,

or 22k + 7m = 1356

Now, the given equations are:

3k + m = 187

22k + 7m = 1356

Substitute m = 187 - 3 k in second equation ,we get

22k + 7m = 1356  ⇒ 22 k + 7 ( 187 - 3 k)  = 1356

⇒ k = 47

⇒ m = 187 - 3 k = 187 - 3(47)=  46, or m = 46

Hence, the number of children in theater   = 2  k = 2 (47) = 94

The number of students in the theater = m = 46

The number of adults in theater =  k  = 47