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Melanie paid $42.50 for 3 adult tickets and 2 student tickets at Theater A. Drew paid $47 for 4 student tickets and 2 adult tickets at Theater A. Theater B charges $9 for each adult ticket and $7 for each student ticket.
Which of the following statements is TRUE?
A
The price for each adult ticket is the same at both theaters

B
The price for each student ticket is the same at both theaters.

C
The price of an adult ticket at Theater A is $0.50 less than the price of an adult ticket at Theater B.

D
The price of a student ticket at Theater B is $0.50 less than the price of a student ticket at Theater A.

Respuesta :

Answer:

B. The price for each student ticket is the same at both theaters

Correct Option is B.

System of Linear equations:

A system of linear equations is a set of equations which are satisfied by the same set of variables.

Ex : 2x - y = 12 , x - 2y = 48

Here,

Let's take adult ticket price in theatre A = x

And the student ticket price in theatre A = y

So, (Given), 3x + 2y = $42.50 (Melanie paid)

=> 2y = $42.50 - 3x --(1)

Also given, 2x + 4y = $47 (Drew paid)

=> 4y = $47 - 2x

2(2y) = $47 - 2x

Now, substitute 2y value from eq-(1), we get

2($42.50 - 3x) = $47 - 2x

$85 - 6x = $47 - 2x

=>  $85 - $47 = 6x - 2x

=> $38 = 4x

=> x = ($38)/4 => 9.5

Substitute x value in eq-(1), we get

2y = $42.50 - 3(9.5) => y = $7.

In the given options only Option B is the correct answer.

Learn more about system of linear equations here:

https://brainly.com/question/21292369?referrer=searchResults

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