Question

A theatre sells a total of 450 Children’s Tickets (x) for $4, Senior Tickets (y) for $7, and Adult Tickets (z) for $9 and collect $3,250. Then the number of children’s tickets sold is 55 more than the number of Senior Tickets.

The augmented matrix is of the form:
[A B C|D]
[E F G|H]
[J K L|M]
See the attached for the rest of the problem.

Answer 1

`\left[\begin{array}cccA&B&C&D\\E&F&G&H\\J&K&L&M\end{array}\right] =\left[\begin{array}ccc1&1&1&450\\4&7&9&3250\\1&-1&0&55\end{array}\right]`

Explanation:

You want the augmented matrix that represents the equations for the number of each kind of ticket sold if 450 tickets costing 4, 7, and 9 dollars were sold for $3250, with 55 more $4 tickets being sold than $7 tickets.

Equations

The problem statement gives rise to these equations, where c, s, a represent numbers of Children's, Senior, and Adult tickets sold, respectively.

c + s + a = 450 . . . . . . . . . total number of tickets sold

4c +7s +9A = 3250 . . . . . revenue from ticket sales

c - s = 55 . . . . . . . . . . . . difference in numbers of tickets

Augmented matrix

The coefficients of these equations are listed in matrix form to give the augmented matrix for the problem. That matrix is shown in the Answer section, above.

Solution

The attachment shows the solution to the problem to be that sales were ...

• 130 Children's tickets
• 75 Senior tickets
• 245 Adult tickets