Respuesta :
Given
A local theater sold 187 tickets to a matinee play with a total revenue of $1,452.00 where they changed $11.00 for adult ticket and $6.00 for a child’s ticket.
Use the variables a and c to represent the number of adult tickets sold and the number of children’s tickets sold respectively.
To determine a system of equations that describes the solution.
1) Enter the equations below separated by a comma.
2) How many adult tickets were sold?
3) How many children’s tickets were sold?
Explanation:
It is given that,
The total number of tickets sold is 187.
The total revenue is $1,452.00.
Since a and c represent the number of adult tickets sold and the number of children’s tickets sold respectively.
Then,
[tex]\begin{gathered} a+c=187\text{ \_\_\_\_\_\_\_\lparen1\rparen} \\ 11a+6c=1452\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Solving (1) and (2) implies,
[tex]\begin{gathered} a=187-c \\ \Rightarrow11(187-c)+6c=1452 \\ \Rightarrow2057-11c+6c=1452 \\ \Rightarrow-5c=1452-2057 \\ \Rightarrow-5c=-605 \\ \Rightarrow c=\frac{605}{5} \\ \Rightarrow c=121 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} a=187-c \\ a=187-121 \\ a=66 \end{gathered}[/tex]Therefore,
1) The equations are,
[tex]a+c=187,11a+6c=1452[/tex]2) The number of adults ticket sold is 66.
3) The number of Children's ticket sold is 121.
