Question

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. Using the variables a and c to represent the number of adult tickets sold and the number of children’s tickets sold respectively, 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?

Answer 1

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?

Step-by-step 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,

`\begin{gathered} a+c=187\text{ \_\_\_\_\_\_\_\lparen1\rparen} \\ 11a+6c=1452\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}`

Solving (1) and (2) implies,

`\begin{gathered} a=187-c \\ \Rightarrow11(187-c)+6c=1452 \\ \Rightarrow2057-11c+6c=1452 \\ \Rightarrow-5c=1452-2057 \\ \Rightarrow-5c=-605 \\ \Rightarrow c=(605)/(5) \\ \Rightarrow c=121 \end{gathered}`

That implies,

`\begin{gathered} a=187-c \\ a=187-121 \\ a=66 \end{gathered}`

Therefore,

1) The equations are,

`a+c=187,11a+6c=1452`

2) The number of adults ticket sold is 66.

3) The number of Children's ticket sold is 121.