Question

You have $110 to spend at the mall. You want to buy at most 6 articles of clothing. A clothing store sells shirts for $12 and pairs of pants for $18. You want to have at least $20 left over for food.
a. Write and graph a system of linear inequalities that represents this situation.

b. How many shirts and pairs of pants can you buy at the store?

Answer 1

Answer:

Part a) The graph in the attached figure (see the explanation)

Pat b)  see the explanation

Step-by-step explanation:

Part a)  Write and graph a system of linear inequalities that represents this situation

Let

x ----> the number of shirts you can buy

y ----> the number of pants you can buy

we know that

The word "at most" is the same that " less than or equal to"

The word "at least" is the same that " greater than or equal to"

so

$x+y \leq 6$ ----> inequality A

The amount you have to spend minus the number of shirts multiplied by its price minus the number of pants multiplied by its price must be greater than or equal to $20

$110-12x-18y \geq 20$

Rewrite

$12x+18y\leq 90$ ----> inequality B

using a graphing tool

see the attached figure

Part b) How many shirts and pairs of pants can you buy at the store?

The solution of the system of inequalities is the shaded area

The solution is all whole numbers included in the shaded area

Example

(0,5),(3,3),(6,0), (3,2),...