Question

A total of 165 people attended the opening night of a school play. Adults were charged $6, and children were charged $2. The total amount of money collected was $618. Which augmented matrix represents the situation?

Answer 1

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Given Information
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Total number of people = 165
Adult = $6
Child = $2
Total collected = $618

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Assumptions 
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Let x be the number of adults and y be the number of children

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Form equations
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Total number of people
x + y = 165
Total amount collected 
6x + 2y = 618

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Ans: The two equations are x + y = 165 and 6x + 2y = 618
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The question is not asking for it but if you need to solve the equation to find the answer to x and y

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Present the two equations and solve for x and y
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x + y = 165          ------------------------- (eqn 1)
6x + 2y = 618      ------------------------- (eqn 2)

(eqn 1) : 
x + y = 165
x = 165 - y -------------------------  substitute into (eqn 2)

6(165 - y) + 2y = 618
990 - 6y + 2y = 618
4y = 990 - 618
4y = 372
y = 93 -------------------------  substitute into (eqn 1)

x + y = 165
x + 93 = 165
x = 165 - 93
x = 72 

x = 72 and y = 93

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Ans: 72 adults and 93 children
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Answer 2

Answer:

$\begin{bmatrix}1 & 1|165\\ 6 & 2|618\end{bmatrix}$

Step-by-step explanation:

A total of 165 people attended the opening night of a school play.

Let there were adults = x  and number of children = y

So x + y = 165 ----------(1)

Now we know adults were charged $6 and children $2.

The total amount collected $618

so  6x + 2y = 618 ----------(2)

Now the augmented matrix for the system of equations will be $\begin{bmatrix}1 & 1|165\\ 6 & 2|618\end{bmatrix}$