Respuesta :
Answer:
The total number of child ticket sold = 87
The total number of adult ticket sold = 128
Step-by-step explanation:
Given - The local theatre performed a Saturday matinee to a crowd of 215 people. Tickets cost $11 child and $15 per adult, bringing in a total of $2877.
To find - Use an inverse matrix to determine the number of each type of ticket sold .
Proof -
Let the total number of child ticket sold = x
Let the total number of adult ticket sold = y
Given that, The local theatre performed a Saturday matinee to a crowd of 215 people.
⇒x + y = 215
Also,
Given that, Tickets cost $11 child and $15 per adult, bringing in a total of $2877
⇒11x + 15y = 2877
So,
The equations becomes
x + y = 215
11x + 15y = 2877
So,
The matrix form becomes
[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}215\\2877\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}1&1\\11&15\end{array}\right| \left\begin{array}{ccc}215\\2877\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&4\end{array}\right| \left\begin{array}{ccc}215\\512\end{array}\right ] \\\left[\begin{array}{ccc}1&1\\0&1\end{array}\right| \left\begin{array}{ccc}215\\128\end{array}\right ]\\\left[\begin{array}{ccc}1&0\\0&1\end{array}\right| \left\begin{array}{ccc}87\\128\end{array}\right ][/tex]
By comparing, we get
x = 87
y = 128
So, we get
The total number of child ticket sold = x = 87
The total number of adult ticket sold = y = 128
