Question

Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wants the number of pencils to be greater than or equal to the square of 3 less than the number of pens.

Create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

A.) Part of the solution region includes a negative number of pencils; therefore, all solutions are not viable for the given situation.


B.) None of the solution region is viable because there cannot be a negative number of pens or pencils.


C.) The entire solution region is viable.


D.) Part of the solution region includes a negative number of pens; therefore, not all solutions are viable for the given situation.

Answer 1

D.) Part of the solution region includes a negative number of pens; therefore, not all solutions are viable for the given situation.

Explanation:

Answer 2

Let
x-------------> the number of pens
y-------------> the number of pencils

we know that
x+y <=25
y>=(x-3)²

using a graph tool
see the attached figure

the viable solution is the area bounded by the four points

the answer is the option
D.) Part of the solution region includes a negative number of pens; therefore, not all solutions are viable for the given situation.