Q:

# A movie theater has a seating capacity of 187. The theater charges $5.00for children,$7.00 for students, and $12.00 of adults. There are half asmany adults as there are children. If the total ticket sales was$ 1356, Howmany children, students, and adults attended?​

Accepted Solution

A:
Answer:Number of children in theater   = 94Number of students   = 46Number of adults in theater= 47Step-by-step explanation:Total seating capacity in the theater = 187Let us assume the number of students in the theater = mand assume  the number of children in the theater = 2kSo, 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 = 187Cost of 1 adult ticket = $12So, the cost of k adult tickets = 12 x (k) =$12kCost of 1 student ticket = $7So, the cost of m student ticket = 7 x (m) =$7mCost of 1 children  ticket = $5So, the cost of 2k children tickets = 5 x (2k) =$10k⇒ 12k  + 10k + 7m =  1356, or 22k + 7m = 1356Now, the given equations are:3k + m = 18722k + 7m = 1356Substitute m = 187 - 3 k in second equation ,we get22k + 7m = 1356  ⇒ 22 k + 7 ( 187 - 3 k)  = 1356⇒ k = 47⇒ m = 187 - 3 k = 187 - 3(47)=  46, or m = 46Hence, the number of children in theater   = 2  k = 2 (47) = 94The number of students in the theater = m = 46The number of adults in theater =  k  = 47