Question

A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the remaining seats to be recliners. If x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities? x + y ≤ 50 x ≥ 20

Answer 1

Answer:

The below graph represents the solution.

Step-by-step explanation:

Here, x represents the number of stools and y represents the number of recliners,

∵ total seats ≤ 50

⇒ x + y ≤ 50,

Also, owner wants at least 20 of the seats to be stools,

i.e. x ≥ 20,

And, the remaining seats to be recliners.    

Related equation of the inequality x + y ≤ 50,

x + y = 50

if x = 0, y = 50

if y = 0, x = 50,

So, join the points (0, 50) and (50, 0) in the coordinate plan,

0 + 0 ≤ 50, ( true )

Thus, the shaded region will contain the origin.

For graphing x ≥ 20,

Shade the region left side of the line x = 20.

By above explanation,

We obtain the feasible region that shows the solution to the system of inequalities. ( shown below )

Note : numbers of thing can not be negative,

i.e. x ≥ 0 and y ≥ 0

Answer 2

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of stools

y ----> the number of recliners

we know that

$x+y \leq 50$ -----> inequality A

$x\geq 20$ ----> inequality B

using a graphing tool

The solution is the triangular shaded area (remember that the number of seats cannot be a negative number)

see the attached figure