11. Let the Number of Students filled in One Van be : V
Let the Number of Students filled in One Bus be : B
Given : The Senior Class of High School A rented and filled 8 Vans and 3 Buses with 150 students
⇒ 8V + 3B = 150 --------------- [1]
Given : The Senior Class of High School B rented and filled 10 Vans and 3 Buses with 162 students
⇒ 10V + 3B = 162 --------------- [2]
Subtracting Equation [1] from Equation [2], we get :
⇒ (10V + 3B) - (8V + 3B) = 162 - 150
⇒ 10V - 8V + 3B - 3B = 12
⇒ 2V = 12
⇒ V = 6
Substituting V = 6 in Equation [1], We get :
⇒ 8(6) + 3B = 150
⇒ 48 + 3B = 150
⇒ 3B = 150 - 48
⇒ 3B = 102
⇒ B = 34
⇒ Each Van can carry 6 Students
⇒ Each Bus can carry 34 students
12 . Let the Price of One Adult Ticket be : A
Let the Price of One Student Ticket be : S
Given : On the First Day, The School sold 6 Adult tickets and 7 student tickets for a Total of $122
⇒ 6A + 7S = 122 ----------- [1]
Given : On the Second Day, The School sold 6 Adult tickets and 6 student tickets for a Total of $114
⇒ 6A + 6S = 114 ----------- [2]
Subtracting Equation [2} from Equation [1], We get :
⇒ (6A + 7S) - (6A + 6S) = 122 - 114
⇒ 6A - 6A + 7S - 6S = 8
⇒ S = 8
Substituting S = 8 in Equation [1], We get :
⇒ 6A + 7(8) = 122
⇒ 6A + 56 = 122
⇒ 6A = 122 - 56
⇒ 6A = 66
⇒ A = 11
⇒ Price of One Adult Ticket = $11
⇒ Price of One Student Ticket = $8