Question

The box office at a movie theater sold 346 tickets for the evening show, and collected $2,980. Howmany $10 adult and how many $5 child tickets were sold?Number of adult tickets sold =Number of child ticket sold

Answer 1

250 adult tickets sold

96 child tickets sold

1) We can solve this problem by resorting to a Linear System of Equations.

2) To do that, let's call a adult and c for the children. The first equation relates the costs and the revenue:

`10a+5c=2980`

And for the second equation, the total number of tickets.

`a+c=346`

3) So now, let's set this up and solve it by using the Elimination Method

`\begin{gathered} 10a+5c=2980 \\ a+c=346\:\:*(-5) \\ \\ 10a+5c=2980 \\ -5a-5c=-1730 \\ ----------- \\ 5a=1250 \\ \\ (5a)/(5)=(1250)/(5) \\ \\ a=250 \\ \\ \end{gathered}`

To find c we can plug a=250 into the second equation

`\begin{gathered} a+c=346 \\ \\ 250+c=346 \\ \\ -250+250+c=346-250 \\ \\ c=96 \end{gathered}`

4) Thus, the answer is:

250 adult tickets sold

96 child ticket sold