Question

A local theater sold 182 tickets to a matinee play with a total revenue of $ 2,662.00 where they charged $21.00 for an adult ticket and $ 11.00 for a child’s ticket. (a)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 situation.Enter the equations below separated with a comma(b)How many adult tickets were sold?(c)How many children’s tickets were sold?

Answer 1

Let:

• The number of adult tickets sold = a;

,

• The number of children’s tickets sold = c

The local theater sold 182 tickets, therefore:

`a+c=182\cdots(1)`

• They charged ,$21.00 for an adult ticket, and ,$11.00 for a child’s ticket,.

,

• The total revenue = $2,662.00

`\implies21a+11c=2662\cdots(2)`

(a)The system of equations is:

`\begin{gathered} a+c=182\cdots(1) \\ 21a+11c=2662\cdots(2) \end{gathered}`

(b)

Next, we solve for the number of adult tickets sold.

From equation (1): c=182-a

Substitute c=182-a into equation (2).

`\begin{gathered} 21a+11c=2662 \\ 21a+11(182-a)=2662 \end{gathered}`

Solve the equation for a.

`\begin{gathered} 21a+2002-11a=2662 \\ 21a-11a=2662-2002 \\ 10a=660 \\ a=(660)/(10) \\ a=66 \end{gathered}`

66 adult tickets were sold.

(c)Finally, we find out how many children's tickets were sold.

Recall: c=182-a

`c=182-a=182-66=116`

116 children's tickets were sold.

Answer:

• (A) a+c=182, 21a+11c=2662

,

• (B)a=66

,

• (C)c=116