Answer:
Number of adults = 7
Number of children = 16
Step-by-step explanation:
Tickets for a play cost 2 pounds for a child, and 4 pounds for an adult.
Let x number of adults and y number of children.
1 child ticket cost = 2 pound
y children ticket cost = 2y pound
1 adult ticket cost = 4 pound
x adults ticket cost = 4x pound
Total number of ticket sales were 60 pounds
Therefore, 4x + 2y = 60 ------------- (1)
One adult brought 4 children with him and the remaining adults each brought 2 children with them.
Remaining number of adult whose brought 2 children = x-1
Number children = 2(x-1)
Total number of children = 2(x-1)+4
Therefore, y=2x+2 ---------------------(2)
System of equation,
2x + y = 30
-2x + y = 2
Using augmented matrix to solve system of equation.
[tex]\begin{bmatrix}2&1&\ |30\\-2&1&|2\end{bmatrix}\\\\R_2\rightarrow R_2+R_1\\\\\begin{bmatrix}2&1& |30\\0&2&|32\end{bmatrix}\\\\R_2\rightarrow\dfrac{1}{2}R_2\\[/tex]
[tex]\begin{bmatrix}2&1&\ |30\\0&1&|16\end{bmatrix}\\\\R_1\rightarrow R_1-R_2\\\\\begin{bmatrix}2&0&\ |14\\0&1&|16\end{bmatrix}\\\\\\[/tex]
[tex]R_1\rightarrow \dfrac{1}{2}R_1\\\\\begin{bmatrix}1&0&|7\\0&1&|16\end{bmatrix}\\\\[/tex]
Now, we find the value of variable.
[tex]x=7\text{ and }y=16[/tex]
Hence, Number of adults are 7 and Number of children are 16.
