Write the Word or Phrase That Best Completes Each Statement

Multiple Choice

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-An accountant checks the reported earnings for a concert venue for three different performers against the number of tickets sold. $\begin{array}{ccccc}\text { Performer } & \begin{array}{c}\text { Children } \\\text { Tickets }\end{array} & \begin{array}{c}\text { Student } \\\text { Tickets }\end{array} & \begin{array}{c}\text { General } \\\text { Admission }\end{array} & \begin{array}{c}\text { Total } \\\text { Revenue }\end{array} \\\mathbf{1} & 1,000 & 250 & 1,000 & \$ 24,750 \\\mathbf{2} & 400 & 300 & 300 & \$ 10,700 \\\mathbf{3} & 400 & 300 & 300 & \$ 8,700\end{array}$
Let $x , y$ , and $z$ represent the cost for children tickets, student tickets, and general admission tickets, respectively. Set up an augmented matrix for the system and solve for $x , y$ , and $z$ . Explain what the accountant knows about the reported earnings.

A) { } ; The system of equations reduces to a contradiction. There are no values for $x , y$ , and $z$ that can simultaneously meet the conditions of this problem.
B) $\{ ( 7,7,16 ) \}$ ; There were $\$ 7$ children's tickets, $\$ 7$ student tickets, and $\$ 16$ general admission tickets sold.
C) $\{ ( 8,8,17 ) \}$ ; There were $\$ 8$ children's tickets, $\$ 8$ student tickets, and $\$ 17$ general admission tickets sold.
D) $\{ ( 6,6,15 ) \}$ ; There were $\$ 6$ children's tickets, $\$ 6$ student tickets, and $\$ 15$ general admission tickets sold.