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