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.

Answer 1

For this case, the first thing we must do is define variables.
 We have then:
 x: number of pens
 y: number of pencils
 We now write the system of inequations:
 $x + y \leq 25 y \geq (x - 3) ^ 2$
 The solution to the system of inequations is given by the shaded region.
 Note: see attached image.