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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4 and each adult ticket sells for $8. There was a total of $640 in revenue from the sale of 100 total tickets. Graphically solve a system of equations in order to determine the number of student tickets sold, x, and the number of adult tickets sold, y.

Respuesta :

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Answer:

number of student tickets sold (x) = 40

number of adult tickets sold (y) = 60

Step-by-step explanation:

Let x = number of student tickets sold

Let y = number of adult tickets sold

Given:

  • total ticket sales = 100

⇒ x + y = 100

Given:

  • student ticket = $4
  • adult ticket = $8
  • total ticket sales = $640

⇒ 4x + 8y = 640

Rewrite  x + y = 100  to make x the subject:

⇒ x = 100 - y

Substitute  x = 100 - y  into  4x + 8y = 640  and solve for y:

⇒ 4(100 - y) + 8y = 640

⇒ 400 - 4y + 8y = 640

⇒ 4y = 240

⇒ y = 60

Substitute found value for y into x = 100 - y and solve for x:

⇒ x = 100 - 60

⇒ x = 40

To solve graphically, rewrite both equations to make y the subject:

y = 100 - x

y = 80 - (1/2)x

Plot both lines.

The solution is the point of intersection (40, 60)

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