Answer:
Part a) [tex]x+y < 400[/tex]
Part b) The graph in the attached figure
Part c) see the explanation
Part d) The number of seat tickets sold must be less than 300 tickets
Step-by-step explanation:
Part a) write an inequality to describe the constraints. specify what each variable represents
Let
x ----> number of lawn tickets sold
y ----> number of seat tickets sold
we know that
The sum of the number of lawn tickets sold plus the number of seat tickets sold must be less than 400 tickets
so
The linear inequality that represent this situation is
[tex]x+y < 400[/tex]
Part b) use graphing technology to graph the inequality. sketch the region on the coordinate plane
we have
[tex]x+y < 400[/tex]
using a graphing tool
The solution is the triangular shaded area of positive integers (whole numbers) of x and y
see the attached figure
Remember that the values of x and y cannot be a negative number
Part c) name one solution to the inequality and explain what it represents in that situation
we know that
If a ordered pair lie on the solution of the inequality, then the ordered pair is a solution of the inequality (the ordered pair must satisfy the inequality)
I take the point (200,100)
The point (200,100) lie on the triangular shaded area of the solution
Verify
Substitute the value of x and the value of y in the inequality and compare the result
For x=200,y=100
[tex]x+y < 400[/tex]
[tex]200+100 < 400[/tex]
[tex]300 < 400[/tex] --> is true
so
The ordered pair satisfy the inequality
therefore
The ordered pair is a solution of the inequality
That means ----> The number of lawn tickets sold was 200 and the number of seat tickets sold was 100
Part d) if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?
we have that
x=100
substitute in the inequality
[tex]100+y < 400[/tex]
solve for y
subtract 100 both sides
[tex]y < 400-100[/tex]
[tex]y < 300[/tex]
therefore
The number of seat tickets sold must be less than 300 tickets
