Answer:
25x + 15y ≤ 285
x + y ≥ 16
Step-by-step explanation:
Let's call x the number of tables that Jack will buy and y the number of chairs that Jack will buy.
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.