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6. Peggy Carter is selling tickets to see Captain America. On the first night she sold 12 adult tickets and 11 student tickets for $301 dollars. One the second night she made $134 selling 6 adult tickets and 4 student tickets. What is the price of the student tickets

Sagot :

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Answer:

student ticket = $11

(adult ticket = $15)

Step-by-step explanation:

Let a = price of adult ticket

Let s = price of student ticket

Given:

  • On the first night she sold 12 adult tickets and 11 student tickets for $301 dollars

⇒ 12a + 11s = 301

Given:

  • On the second night she made $134 selling 6 adult tickets and 4 student tickets

⇒ 6a + 4s = 134

Multiply 6a + 4s + 134 by 2 then subtract from 12a + 11s = 301 to eliminate a:

⇒ (6a + 4s = 134) × 2:  12a + 8s = 268

  12a + 11s = 301

- (12a + 8s = 268)

--------------------------

            3s = 33

     

⇒ s = 33 ÷ 3 = 11

Substitute found value of s into one of the equations and solve for a:

⇒ 12a + 11(11) = 301

⇒ 12a + 121 = 301

⇒ 12a = 180

⇒ a = 15

Therefore, the price of an adult ticket is $15 and the price of a student ticket is $11

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