Question

Two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. fewer than 400 tickets in total were sold.

Answer 1

Answer:

Part a) $x+y < 400$

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

$x+y < 400$

Part b) use graphing technology to graph the inequality. sketch the region on the coordinate plane

we have

$x+y < 400$

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

$x+y < 400$

$200+100 < 400$

$300 < 400$ --> 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

$100+y < 400$

solve for y

subtract 100 both sides

$y < 400-100$

$y < 300$

therefore

The number of seat tickets sold must be less than 300 tickets