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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

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