Question

rasheed is buying wings and quesadillas for a party. A package of wings costs $8. A package of quesadillas costs $10. He must spend no more than $160. Rasheed's freezer will hold a maximum of 20 packages of wings and quesadillas. PART B: Graph the systems of linear inequalities and shade where the solutions are.

Answer 1

4 packages of wings and 4 packages of quesadillas

Answer 2

Answer:

Step-by-step explanation:

A system of inequalities of two variables is a set of inequalities of two variables that act at the same time, that is, the solution points must meet all the inequalities of the system.

Then you must first define what the system variables will be. You know that Rasheed is buying wings and quesadillas for a party. Then your variables will be:

• w: number of package of wings bought by Rasheed.
• q: quantity of package of quesadillas bought by Rasheed.

You know too that a package of wings costs $8 and a package of quesadillas costs $10. Then $ 8*w and $ 10*q will be the price paid for the amount of packages bought from wings and quesadillas by Rasheed respectively. If he must spend no more than $160 between winds and quesadilla, so:

8*w + 10*q ≤ 160

On the other hand, Rasheed's freezer will hold a maximum of 20 packages of wings and quesadillas.  So the quantity of packages of wings and quesadillas bought by Rasheed should not exceed the quantity of 20.

Therefore, w + q ≤ 20

Finally, the system of linear inequalities is:

$\left \{ {{8*w+10*q\leq 160} \atop {w+q\leq 20}} \right.$

To find the solution of the system, look for the solutions of each of the inequalities of the system and look at the regions where they will coincide.

That is, a possible method of finding common regions among all inequalities is to first find each region of each inequality. Then all the solutions are drawn on the same plane. The regions thus overlap, being able to easily see which regions will be a system solution.

In the attached image you can see the graph of both inequations. One region is marked green, belonging to the inequality w + q ≤ 20, while the other region is marked violet, belonging to the inequality 8*w + 10*q ≤ 160.

The areas where it is shaded by both colors, this is the intersection of the regions solutions, will be the solutions of the inequality system.