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Part A
At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75.
Neil bought one ticket, three drinks, and two bags of popcorn for $27.75
Jung bought two tickets, two drinks, and one bag of popcorn for $34.
Determine the values that replace the letters in the augmented matrix which represents the situation.
3
a
c с
3
1 b
d 27.75
1 f
Le
2
a =
b=
C =
d =
e =

Answer :

The augmented matrix for the system is:

[tex]\left[\begin{array}{cccc}3&1&1&43.75\\1&3&2&27.75\\2&2&1&34\end{array}\right][/tex]

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For our system, we suppose that x is the number of tickets, y is the number of drinks and z is the number of bags of popcorn.

Devin bought three tickets, one drink, and one bag of popcorn for $43.75.

This means that:

[tex]3x + y + z = 43.75[/tex]

Neil bought one ticket, three drinks, and two bags of popcorn for $27.75.

This means that:

[tex]x + 3y + 2z = 27.75[/tex]

Jung bought two tickets, two drinks, and one bag of popcorn for $34.

This means that:

[tex]2x + 2y + z = 34[/tex]

The system is:

[tex]3x + y + z = 43.75[/tex]

[tex]x + 3y + 2z = 27.75[/tex]

[tex]2x + 2y + z = 34[/tex]

Which is represented by the following augmented matrix:

[tex]\left[\begin{array}{cccc}3&1&1&43.75\\1&3&2&27.75\\2&2&1&34\end{array}\right][/tex]

A similar problem is given at https://brainly.com/question/13266649

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