Suppose that you can spend $72 for compact discs and videos. Discs cost $18 and videos cost $9 each. write a system of inequalities that shows the various number of discs and videos that you can buy.
18x + 9y ≤ 72
To write a system of inequalities that represents the number of compact discs (D) and videos (V) you can buy, we need to consider the given information:
1. The total amount you can spend is $72.
2. The cost of a disc is $18.
3. The cost of a video is $9.
Let's establish the inequalities based on these conditions:
1. Inequality for the total amount spent:
$18D + $9V ≤ $72
The left side of the inequality represents the cost of the discs and videos you buy, while the right side represents the maximum amount you can spend.
2. Inequalities for the individual number of discs and videos:
D ≥ 0 (Because you cannot buy a negative number of discs)
V ≥ 0 (Similarly, you cannot buy a negative number of videos)
These inequalities ensure that both D and V are non-negative since the number of items cannot be negative.
In summary, the system of inequalities is:
$18D + $9V ≤ $72
D ≥ 0
V ≥ 0
These inequalities represent the different combinations of the number of discs and videos you can buy while remaining within your budget.