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

The student is looking for the augmented matrix that represents the system of equations based on the ticket sales for the school play, which can be formatted as a 2x3 matrix: [[1, 1, 165], [6, 2, 618]].

Step-by-step explanation:

The student is asking for the augmented matrix that represents the situation involving ticket sales for a school play. There are two things we know: the total number of people (165) and the total amount of money collected ($618). Adults are charged $6 and children $2 per ticket. We can set up the following two equations from this information:

• Let A represent the number of adults, and C represent the number of children.
• The first equation (representing the total number of attendees) will be: A + C = 165
• The second equation (representing the total amount of money collected) will be: 6A + 2C = 618

The augmented matrix that represents this system of equations is:

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

This matrix holds the coefficients and constants of the system of linear equations described by the ticket sale situation.