Question

Lincoln Middle School has a total of $200 to spend on notebooks and tablets for the school board meeting. Notebooks cost $7 each, and tablets cost $5 each.

If x represents the number of notebooks and y represents the number of tablets, which graph correctly shows the solution to the problem?
http://prntscr.com/btbjuj
http://prntscr.com/btbjzb

Answer 1

@Ciarán95

Answer 2

28 notebooks and 40 tablets.

Answer 3

Would it be A? @Ciarán95

Answer 4

is it a?

Answer 5

I don't think Option A is correct here. The inequality for the problem appears to be:

\[7x + 5y \le 200\]

where x = Number of Notebooks and y = Number of Tablets, x, >=0, y >= 0 (i.e. we can't buy a negative number of either). I'm not sure why the negative parts of the x and y axis are also highlighted, as they shouldn't really be relevant to this problem.

If we look at Option B and pick a point within the highlighted region, say x = 10, y = 10 and plug in these values into our inequality:

\[7(10) + 5(10) \le 200\]
\[70 + 50 \le 200\]
\[150 \le 200, which~is~true\]

We can repeat this with any point highlighted within the region and our inequality will hold (i.e. under or equal to the budget limit).

If we look at option A though, for example and pick any point within the shaded region (say x = 20, y = 30):

\[7(20) = 5(30) \le 200\]
\[140 + 150 \le 200\]
\[290 \le 200, which~is~false\]

As with Option B, we can pick any point which also lies in the shaded region and get the same result as above (i.e. over the $200 budget limit).

Answer 6

Sorry @OswaldMurphy, I meant to say that I'm not sure if Option A is correct here!!

I assume that option C and D are equivalent to A and B, except that the dotted line indicates we are not including points which lie on it, only those which lie above/below it. The line seems to pass through the x-axis at around x = 29 and the y-axis at y = 40. If we plug in the values (29, 0) our equality won't hold, but it will with (0, 40).

So, I'm not sure whether we can include the points which lie on the line itself, but I would say the answer is either A or D if that's any help to you! :)