Question

The drama club is selling tickets to its play.
An adult ticket costs $15 and a student ticket
costs $11. The auditorium will seat 300 ticket-hol
ders. The drama club wants to collect at least
$3630 from ticket sales.
a) Write and graph a system of four inequalities
that describes how many of each ty
pe of
ticket the club must sell to meet
its goal.
b) List three different combinations of tickets
sold that satisfy the inequalities

Someone please show me how to do this I have like 15 more problems like this and just need someone to show me how.....................

Answer 1

Let A=# of adult tickets sold, and S=# of student tickets sold.

Now start thinking about the restrictions given by the problem.
The seating limit is 300, so need \[A+S \le300\]
To collect at east $3630, need the total revenue to be at least that much. The total revenue is the sum of the price of each ticket x # tickets sold:\[15A+11S \ge3630\]
I'm not sure where the other 2 inequalities come in, unless it's getting at
\[A \ge0, S \ge0\]

Answer 2

@DebbieG how would i graph this? also what would be 3 different combinations that of tickets that satisfy the inequalities? thanks so much!!!!!!!!

Answer 3

@satellite73

Answer 4

Make your axes A and S.... I don't think it really matters which is which, but then just solve each of the first 2 inequalities for your horizontal axis variable, which gives you a linear equation. E.g., if you put A on the horizontal axis, the first boundary line is A=-S+300, a line with slope =-1 and y-intercept of 300. Do the same with the 2nd equation. The other 2 will just be the axes, e.g., you must be to the right of the vertical axes and above the horizontal axis - so in the first quandrant.

Once you have those boundary lines in place, shade in the parts that satisfy each inequality. E.g, the "less than" inequality means you will be "below" that line, the "greater than" means you will be "above". This will show you where your solutions lie - then just pick 3 points in that region and try them.