Question

suppose you are buying CDs and DVDs from AMAZON for gifts CDs cost $4 each and DvDs cost 8$ each you want to spend less than 40$ on all of the gifts you need at least 4 gifts altogether graph a system of linear inequalities to model the scenario and give two solutions combinations of CDs and DVDs they could sell to meet their goal

Answer 1

x + y ≤ 4

4x +8y ≤ 40

(1,2) and (2,2) are two possible solutions.

Check the graph below, please.

1) Gathering the data

CD = $4

DVD = $8

budget: $40

2) Notice the word at least. We can write two inequalities, one relating the price of each item and the budget. And the other one relating the number of CDs and DVDs to be bought.

x=CD, y= DVD

x + y ≤ 4 4 CDs and DVDs, altogether

4x +8y ≤ 40 The price of each item, as coefficient and the budget of $40

2.2) Let's plot those inequalities

Let's pick two solutions, for the common region shaded by both graphs.

Like (2, 2) and (1, 2)

3) If we plug into those inequalities we can verify them. So the answers are:

x + y ≤ 4

4x +8y ≤ 40

(1,2) and (2,2) are two possible solutions.