Question

The school that John attends is selling tickets to a student play. The activities department is

selling adult tickets and student tickets. They also plan to sell concessions during the

performance. On the first day of ticket sales, the school sold 12 adult tickets and 14 student

tickets for a total of $ 166.00. The school took in $ 132.00 the second day by selling 4 adult

tickets and 20 student tickets.
Find the price of an adult ticket and the price of a student ticket.
Let x = price of an adult ticket

Let y = price of a student ticket


Please help me i will give you brainliest

Answer 1

Answer:

Given, School sells 2 types of tickets: Student and Adult.

Student Ticket Cost = Rs. y

Adult Ticket Cost = Rs. x

Also it is given that, on the first day, 12 adult tickets were sold and 14 student tickets were sold making a collection of $ 166.00

Writing it in terms of equation we get:

⇒ 12x + 14y = 166

(Dividing by a common factor 2, we get:)

⇒ 6x + 7y = 83  ...(Eqn. 1)

Now, during the second day, 4 adult tickets and 20 student tickets were sold with a collection of $ 132.00.

Writing this in terms of equation,

⇒ 4x + 20y = 132

(Dividing by common factor 4, we get:)

⇒ x + 5y = 33  

⇒ x = ( 33 - 5y )   ...(Eqn. 2)

Substituting the value of 'x' from (Eqn. 2) in (Eqn. 1) we get:

⇒ 6 ( 33 - 5y ) + 7y = 83

⇒ 198 - 30y + 7y = 83

⇒ 198 -  23y = 83

⇒ 23y = 198 - 83

⇒ 23y = 115

⇒ y = 115 ÷ 23

⇒ y = 5

Hence the cost of a Student ticket is $ 5.00.

Substituting the value of 'y' in Eqn. 2, we get:

⇒ x = 33 - 5 ( 5 )

⇒ x = 33 - 25

⇒ x = 8

Hence the value of an Adult ticket is $ 8.00.

Answer 2

Answer:

⠀⠀⠀⌬ 12 adults and 14 students = $ 166

⠀⠀⠀⌬ 4 adults and 20 students = $ 132

Here x is price of an adult ticket and y is price of a student ticket.

• According to the Question :

⇒ 12 adults + 14 students = $ 166

⇒ 12x + 14y = $ 166

⇒ 2(6x + 7y) = $ 166

• Dividing both term by 2

⇒ 6x + 7y = $ 83 — eq. ( I )

⇒ 4 adults + 20 students = $ 132

⇒ 4x + 20y = $ 132

⇒ 4(x + 5y) = $ 132

• Dividing both term by 4

⇒ x + 5y = $ 33 — eq. ( II )

⠀⠀⠀⠀⠀───────────────

• Multiplying eq. ( II ) by 6 and Subtracting eq. ( I ) from eq. ( II ) :

⇢ 6x + 30y = $ 198

⇢ 6x + ⠀7y = $ 83

⠀–⠀⠀–⠀⠀⠀⠀–

_________________

⇢ 23y = 115

⇢ y = 115/23

⇢ y = $ 5⠀⠀⠀⠀「 Student Ticket 」

• Putting value of y in eq. ( II ) :

⇢ x + 5y = $ 33

⇢ x + 5($ 5) = $ 33

⇢ x + $ 25 = $ 33

⇢ x = $ 33 - $ 25

⇢ x = $ 8⠀⠀⠀⠀「 Adult Ticket 」

∴ Hence, Cost of tickets for adult and student is $ 8 and $ 5 respectively.