Jack is buying tables and chairs for his deck party tables cost $25 and chair cost $15 he plans to spend no more than $285 and buy at least 16 items. write a system of inequalities that meet the criteria.Graph and shade the inequalities and then list one solution that makes the situation true.

Then, the total cost for the tables will be $25 times the number of tables or $25x. In the same way, the total cost for the chairs will be $15 times the number of chairs or $15y.

So, if he plans to spend $285 or less, we can write the following inequality:

25x + 15y ≤ 285

Then, If he will buy at least 16 items, the sum of the number of tables x and the number of chairs y will be greater or equal to 16. So:

x + y ≥ 16

So, the system of inequalities that meet the criteria is:

25x + 15y ≤ 285

x + y ≥ 16

Now, to graph the inequalities we need to graph the lines that separate the regions, so we will graph the lines 25x + 15y = 285 and x + y = 16, and then we will find the region that satisfies the inequalities.

So, we will find two points in every line.

For 25x + 15y = 285, we get:

If x = 0 then:

25(0) + 15y = 285

15y = 285

y = 19

If y = 0 then:

25x + 15(0) = 285

25x = 285

x = 11.4

In the same way, for x + y = 16, we get:

If x = 0 then y = 16

If y = 0 then x = 16

So, we have (0, 19) and (11.4, 0) for the first equation and (0, 16) and (16, 0) for the second equation. Therefore, the graph of the lines is:

Where the red line is the first equation and the blue line is the second equation.

Now, we need to identify the region that satisfies the inequality, so let's select a point in every region. So, if we select the point (0, 17), we get:

25x + 15y ≤ 285

25(0) + 15(17) ≤ 285

255 ≤ 285

x + y ≥ 16

0 + 17 ≥ 16

17 ≥ 16

Since both expressions are true, this region is the solution of the system, and (0, 17) makes the situation true.