Question

The manager of a movie theater found that Saturday's sales were $335. He knew that a total for 65 tickets were sold. Adult tickets, a, cost $7, and child tickets, c, cost $4. The system of equations shown can be used to represent the situation.

Answer 1

`\begin{gathered} \text{Given} \\ a+c=65 \\ 7a+4c=335 \end{gathered}`

Solve by substitution, use the first equation and solve in terms of c

`\begin{gathered} a+c=65 \\ c=65-a \end{gathered}`

Substitute this to the second equation and solve for a

`\begin{gathered} 7a+4c=335 \\ 7a+4(65-a)=335 \\ 7a+260-4a=335 \\ 7a-4a=335-260 \\ 3a=75 \\ (3a)/(3)=(75)/(3) \\ a=25 \end{gathered}`

Substitute the value of a back to the first equation

`\begin{gathered} a+c=65 \\ 25+c=65 \\ c=65-25 \\ c=40 \end{gathered}`

With a = 25, and c = 40, we can conclude that there are 25 adult tickets, and 40 child tickets sold on Saturday.